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Serum concentrations of TNF-α and its soluble receptors in Graves' disease
Qing Zhu, Jianbin Su, Xueqin Wang, Mengjie Tang, Yingying Gao, and Dongmei Zhang
Graves' disease (GD), an organ-specific autoimmune disease, is the most common cause of hyperthyroidism. Tumour necrosis factor-alpha (TNF-α) exhibits immunological and metabolic activities involved in the induction and maintenance of immune responses. We attempted to evaluate the relationship between GD and serum TNF-α and its soluble receptors (sTNFRs), soluble TNF receptor 1 and 2 (sTNF-R1 and sTNF-R2). A total of 72 GD patients and 72 matched healthy individuals were recruited for this study. Serum TNF-α and sTNFRs were measured by sandwich ELISA. In our study, no significant difference was observed in TNF-α, but sTNFRs were found to be significantly elevated in GD patients compared to healthy individuals. Serum sTNFR levels were positively correlated with free triiodothyronine (FT3) and free thyroxine (FT4), and TNF-α was negatively correlated with thyroid-stimulating hormone (TSH) in the GD group. It was also shown that thyrotropin receptor antibody (TRAb) was positively correlated with TNF-α and sTNFRs. Spearman's correlation analysis showed that only sTNF-R1 was positively correlated with complement C3. Multiple linear regression analysis suggests that serum levels of sTNF-R1 and FT4 may play an important role in the serum level of FT3. According to the median value of FT3 level, GD patients were further divided into a high FT3 group and a low FT3 group. The serum levels of sTNF-R1 in the high FT3 GD group were significantly higher than those in the low FT3 GD group. In conclusion, sTNFRs may play an important role in anti-inflammatory and immune response in GD.
The association between serum adenosine deaminase levels and Graves' disease
Chun-feng Lu, Wang-shu Liu, Xiao-qin Ge, Feng Xu, Jian-bin Su, Xue-qin Wang, and Yan Wang
Adenosine deaminase (ADA) is essential for the differentiation and maturation of lymphocytes, while lymphocytes infiltration in thyroid tissue is a vital pathological feature of Graves' disease (GD). The aim of the present study was to compare the concentration of ADA between healthy controls (HC) and patients with GD, and evaluate the association between ADA and GD.
A total of 112 GD patients and 77 matched HC were enrolled in this study. Each participant was examined for thyroid hormones and autoantibodies, ADA concentration, and thyroid ultrasonography.
Serum ADA levels in GD patients were significantly higher than that in HC subgroup (P < 0.001). In GD patients, serum ADA levels were positively associated with serum-free triiodothyronine (FT3), free thyroxine (FT4), thyroid peroxidase antibody (TPOAb), thyroid-stimulating hormone receptor antibody (TRAb) levels, and total thyroid gland volume (thyroid VolT) and negatively associated with serum thyroid-stimulating hormone receptor (TSH) levels (all P < 0.05). There were no similar correlations in the HC subgroup. Multiple linear regression analysis suggested that serum TSH, FT3, and ADA levels played an important role in serum TRAb levels.
Our results demonstrated that serum ADA levels were closely associated with GD.
Non-thyroidal illness syndrome predicts outcome in adult critically ill patients: a systematic review and meta-analysis
Josi Vidart, Paula Jaskulski, Ana Laura Kunzler, Rafael Aguiar Marschner, André Ferreira de Azeredo da Silva, and Simone Magagnin Wajner
We performed a systematic review and meta-analysis to comprehensively determine the prevalence and the prognostic role of nonthyroidal illness syndrome (NTIS) in critically ill patients. We included studies that assessed thyroid function by measuring the serum thyroid hormone level and in-hospital mortality in adult septic patients. Reviews, case reports, editorials, letters, animal studies, duplicate studies, and studies with irrelevant populations and inappropriate controls were excluded. A total of 6869 patients in 25 studies were included. The median prevalence rate of NTIS was 58% (IQR 33.2-63.7). In univariate analysis, triiodothyronine (T3) and free T3 (FT3) levels in non-survivors were relatively lower than that of survivors (8 studies for T3; standardized mean difference (SMD) 1.16; 95% confidence interval (CI), 0.41–1.92; I2 = 97%; P < 0.01). Free thyroxine (FT4) levels in non-survivors were also lower than that of survivors (12 studies; SMD 0.54; 95% CI, 0.31–0.78; I2 = 83%; P < 0.01). There were no statistically significant differences in TSH levels between non-survivors and survivors. NTIS was independently associated with increased risk of mortality in critically ill patients (OR = 2.21, 95% CI 1.64.- 2.97, I2 = 65% p < 0.01) The results favor the concept that decreased thyroid function might be associated with a worse outcome in critically ill patients. Hence, the measurement of TH could provide prognostic information on mortality in adult patients admitted to ICU.
Prostate gland as a target organ of thyroid hormones: advances and controversies
Brenda Anguiano, Carlos Montes de Oca, Evangelina Delgado-González, and Carmen Aceves
Thyroid hormones are involved in the development and function of the male reproductive system, but their effects on the prostate have been poorly studied. This work reviews studies related to the interrelationship between the thyroid and prostate. The information presented here is based upon bibliographic searches in PubMed using the following search terms: prostate combined with thyroid hormone or triiodothyronine (T3), thyroxine (T4), hypothyroidism, hyperthyroidism, or deiodinase. We identified and searched 49 articles directly related to the issue, and discarded studies related to endocrine disruptors. The number of publications has grown in the last 20 years, considering that one of the first studies was published in 1965. This review provides information based on in vitro studies, murine models, and clinical protocols in patients with thyroid disorders. Studies indicate that thyroid hormones regulate different aspects of growth, metabolism, and prostate pathology, whose global effect depends on total and/or free concentrations of thyroid hormones in serum, local bioavailability and the endocrine androgen/thyronine context.
Elevated circulating Gpnmb levels are associated with hyperthyroidism
Jiayang Lin, Peizhen Zhang, Yan Huang, Xueyun Wei, Dan Guo, Jianfang Liu, Deying Liu, Yajuan Deng, Bingyan Xu, Chensihan Huang, Xiaoyu Yang, Yan Lu, Lijing Jia, and Huijie Zhang
Glycoprotein non-metastatic protein B (Gpnmb) has been identified as a new cytokine secreted by hepatocyte that plays an important role in balancing lipid homeostasis and development of obesity and metabolic disorders. However, information is not available regarding the association between circulating Gpnmb and hyperthyroid in humans.
We measured serum Gpnmb in 180 hyperthyroid patients and 82 healthy subjects that were recruited from the clinic. Of them, 46 hyperthyroid patients received thionamide treatment for 3 months.
Hyperthyroid subjects had higher levels of circulating Gpnmb than healthy controls (47.8 ± 10.1 ng/mL vs 31.0 ± 4.9 ng/mL, P < 0.001). Subjects with higher levels of serum free triiodothyronine (T3) and free thyroxine (T4) had higher levels of circulating Gpnmb. After thionamide treatment, levels of circulating Gpnmb in hyperthyroid subjects remarkably declined with significant improvement of thyroid function (P < 0.001). Furthermore, the change of circulating Gpnmb levels was significantly associated with basal metabolic rate (BMR) and thyroid hormones, including free T3 and free T4, adjusting for age, gender, smoking and BMI before thionamide treatment. In multivariable logistic regression analyses, circulating Gpnmb was significantly associated with risks of hyperthyroidism (OR (95% CI): 1.44 (1.20–1.74), P < 0.001), adjusted for age, gender, BMI, fasting glucose, HOMA-IR, LDL-cholesterol, ALT and AST.
These findings indicate that circulating Gpnmb concentrations are independently associated with hyperthyroid, suggesting that circulating Gpnmb may be a predictor of risk for hyperthyroidism and can be used for therapeutic monitoring.
Obese patients with higher TSH levels had an obvious metabolic improvement after bariatric surgery
Nannan Bian, Xiaomeng Sun, Biao Zhou, Lin Zhang, Qiu Wang, Yu An, Xiaohui Li, Yinhui Li, Jia Liu, Hua Meng, and Guang Wang
Bariatric surgery has become the most effective treatment for morbid obesity. Increasing evidence showed that bariatric surgery can alleviate insulin resistance and influence thyroid function. This study aimed to investigate the relationship between changes in thyroid function and adipose tissue insulin resistance (adipo-IR) after bariatric surgery.
A total of 287 non-diabetic participants with regular thyroid function were recruited and divided into the lean, overweight and obese groups. Among them, 50 morbidly obese patients submitted to bariatric surgery.
The obese group had a higher level of adipo-IR, thyroid-stimulating hormone (TSH), free triiodothyronine (FT3), FT3/free thyroxine (FT4) and metabolism disorders than the lean and overweight groups. BMI was correlated with TSH, FT3, FT3/FT4 and adipo-IR (r = 0.309, 0.315, 0.322 and 0.651, respectively, all P < 0.001). Adipo-IR was significantly correlated with TSH (r = 0.402, P < 0.001), FT3 (r = 0.309, P < 0.001), and FT3/FT4 (r = 0.228, P < 0.05). Bariatric surgery resulted in a sharp decline in BMI, adipo-IR, TSH, FT3 and FT3/FT4 levels, meanwhile, metabolic disorders improved. The decrease in BMI after bariatric surgery was significantly correlated with reductions in adipo-IR (r = 0.577, P < 0.001) and TSH (r = 0.401, P = 0.005). Interestingly, the fasting blood glucose, fasting insulin, adipo-IR and TSH in the higher TSH group decreased more remarkably than in the lower TSH group.
Obese individuals with higher TSH levels had an obvious metabolic improvement after bariatric surgery.
Maternal adiposity, smoking, and thyroid function in early pregnancy
Stine Linding Andersen, Louise Knøsgaard, Aase Handberg, Peter Vestergaard, and Stig Andersen
A high activity of the deiodinase type 2 has been proposed in overweight, obese, and smoking pregnant women as reflected by a high triiodothyronine (T3)/thyroxine (T4) ratio. We speculated how maternal adiposity and smoking would associate with different thyroid function tests in the early pregnancy.
Cross-sectional study within the North Denmark Region Pregnancy Cohort.
Maternal thyroid-stimulating hormone (TSH), total T4 (TT4), total T3 (TT3), free T4 (fT4), and free T3 (fT3) were measured in stored blood samples (median gestational week 10) by an automatic immunoassay. Results were linked to nationwide registers, and live-birth pregnancies were included. The associations between maternal adiposity (overweight or obese), smoking, and log-transformed TSH, fT3/fT4 ratio, and TT3/TT4 ratio were assessed using multivariate linear regression and reported as adjusted exponentiated β coefficient (aβ) with 95% CI. The adjusted model included maternal age, parity, origin, week of blood sampling, and diabetes.
Altogether 5529 pregnant women were included, and 40% were classified with adiposity, whereas 10% were smoking. Maternal adiposity was associated with higher TSH (aβ 1.13 (95% CI 1.08–1.20)), whereas maternal smoking was associated with lower TSH in the early pregnancy (0.875 (0.806–0.950)). Considering the T3/T4 ratio, both maternal adiposity (fT3/fT4 ratio: 1.06 (1.05–1.07); TT3/TT4 ratio: 1.07 (1.06–1.08)) and smoking (fT3/fT4 ratio: 1.07 (1.06–1.09); TT3/TT4 ratio: 1.10 (1.09–1.12)) were associated with a higher ratio.
In a large cohort of Danish pregnant women, adiposity and smoking showed opposite associations with maternal TSH. On the other hand, both conditions were associated with a higher T3/T4 ratio in early pregnancy, which may reflect altered deiodinase activity.
On the role of gallbladder emptying and incretin hormones for nutrient-mediated TSH suppression in patients with type 2 diabetes
David P Sonne, Asger Lund, Jens Faber, Jens J Holst, Tina Vilsbøll, and Filip K Knop
Bile acids are possible candidate agents in newly identified pathways through which energy expenditure may be regulated. Preclinical studies suggest that bile acids activate the enzyme type 2 iodothyronine deiodinase, which deiodinates thyroxine (T4) to the biologically active triiodothyronine (T3). We aimed to evaluate the influence of bile acid exposure and incretin hormones on thyroid function parameters in patients with type 2 diabetes. Thyroid-stimulating hormone (TSH) and thyroid hormones (total T3 and free T4) were measured in plasma from two human studies: i) 75 g-oral glucose tolerance test (OGTT) and three isocaloric (500 kcal) and isovolaemic (350 ml) liquid meals with increasing fat content with concomitant ultrasonographic evaluation of gallbladder emptying in 15 patients with type 2 diabetes and 15 healthy age, gender and BMI-matched controls (meal-study) and ii) 50 g-OGTT and isoglycaemic intravenous glucose infusions (IIGI) alone or in combination with glucose-dependent insulinotropic polypeptide (GIP), glucagon-like peptide 1 (GLP1) and/or GLP2, in ten patients with type 2 diabetes (IIGI-study). In both studies, TSH levels declined (P<0.01) similarly following all meal and infusion stimuli. T3 and T4 concentrations did not change in response to any of the applied stimuli. TSH levels declined independently of the degree of gallbladder emptying (meal-study), route of nutrient administration and infusion of gut hormones. In conclusion, intestinal bile flow and i.v. infusions of the gut hormones, GIP, GLP1 and/or GLP2, do not seem to affect thyroid function parameters. Thus, the presence of a 'gut–thyroid–pituitary' axis seems questionable.
An analysis of the correlation between thyroid nodules and metabolic syndrome
Ling Hu, Ting Li, Xiao-Ling Yin, and Yi Zou
The purpose of this study was to explore the prevalence of thyroid nodules (TN) and metabolic syndrome (MS) and to analyze the correlation between TN and the components of MS.
A total of 1526 subjects were divided into two groups: a TN group and a non-thyroid nodules (NTN) group. The height, weight, blood pressure, fasting blood glucose level, fasting plasma insulin level, serum lipid profile, uric acid level, serum thyroid-stimulating hormone (TSH) level, free triiodothyronine (FT3) level, and free thyroxine (FT4) level of each patient were measured. Insulin resistance (IR) was estimated by homeostasis model assessment of insulin resistance (HOMA-IR). Fatty liver and TN were detected by color Doppler ultrasonography.
(i) The overall prevalence of TN was 39.5%; it was significantly higher in women than in men (P < 0.01) and progressively increased with age in both sexes. (ii) The overall prevalence of MS was 25.6%; it was significantly higher in men than in women (P < 0.01) and progressively increased with age in both sexes. (iii) FT3 was significantly lower in the TN group than in the NTN group (P < 0.01). (iv) BMI, triglycerides, and HOMA-IR were higher in the TN group than in the NTN group (P < 0.05). (v) The existence of TN was significantly associated with overweight/obesity (OR = 1.03, 95% CI = 1.024–1.089), and with insulin resistance (IR) (OR = 1.98, 95% CI = 1.645–2.368), after adjusting for age and sex.
The prevalence of thyroid nodules and metabolic syndrome in the Nanchang area increases with age, and overweight/obesity and IR in patients are associated with thyroid nodules.
Thyroid states regulate subcellular glucose phosphorylation activity in male mice
Flavia Letícia Martins Peçanha, Reinaldo Sousa dos Santos, and Wagner Seixas da-Silva
The thyroid hormones (THs), triiodothyronine (T3) and thyroxine (T4), are very important in organism metabolism and regulate glucose utilization. Hexokinase (HK) is responsible for the first step of glycolysis, catalyzing the conversion of glucose to glucose 6-phosphate. HK has been found in different cellular compartments, and new functions have been attributed to this enzyme. The effects of hyperthyroidism on subcellular glucose phosphorylation in mouse tissues were examined. Tissues were removed, subcellular fractions were isolated from eu- and hyperthyroid (T3, 0.25 µg/g, i.p. during 21 days) mice and HK activity was assayed. Glucose phosphorylation was increased in the particulate fraction in soleus (312.4% ± 67.1, n = 10), gastrocnemius (369.2% ± 112.4, n = 10) and heart (142.2% ± 13.6, n = 10) muscle in the hyperthyroid group compared to the control group. Hexokinase activity was not affected in brain or liver. No relevant changes were observed in HK activity in the soluble fraction for all tissues investigated. Acute T3 administration (single dose of T3, 1.25 µg/g, i.p.) did not modulate HK activity. Interestingly, HK mRNA levels remained unchanged and HK bound to mitochondria was increased by T3 treatment, suggesting a posttranscriptional mechanism. Analysis of the AKT pathway showed a 2.5-fold increase in AKT and GSK3B phosphorylation in the gastrocnemius muscle in the hyperthyroid group compared to the euthyroid group. Taken together, we show for the first time that THs modulate HK activity specifically in particulate fractions and that this action seems to be under the control of the AKT and GSK3B pathways.


C is for Cookie Monster Brownie Sandwich Cookies! Perfect for Halloween, or for any Sesame Street fan, these cookies are not scary, but sweet. Creamy buttercream frosting sandwiched between two chewy brownies.
Whisk flour, cocoa, baking soda and salt in a bowl. Set aside.
Cream butter and sugar until light and creamy, about 3 minutes. Add egg, milk, and vanilla. Slowly add dry ingredients.
Drop batter by heaping tablespoon onto the prepared baking sheets, 2 inches apart.
After cookies have cooled, spread buttercream icing on one cookie and top with another cookie to make a "sandwich".
Spoon buttercream frosting in a pastry bag and use a star tip to adhere the two candy eyes.


text:
\section{Appendix}
\label{sec:Appendix}
\input{Appendix/Gaussian_integral.tex}

\subsection{Proving Lemma \ref{Lem:Gaussian_integral}}
\label{subsec:Gaussian_integral}
{\bf Lemma \ref{Lem:Gaussian_integral}} (Gaussian Integral)
\textit{ Let $\vb$ and $\xb$ be independent
  Gaussian random vectors with distribution ${\cal N}(\zerob,\Ib_N)$
  each. Then
\be
E\left\{ e^{\eta\left(\|\vb+a \xb\|^2-\|\vb\|^2\right)} \right\} =
  \left(\frac{1}{1-2a^2\eta(1+2\eta)}\right)^{N/2} \ .
\ee

\noindent {\bf Proof:}
In order to determine the expected value we compute the multivariate integral
\begin{align*}
& E \left\{e^{\eta\left(\|\vb+a \xb\|^2-\|\vb\|^2\right)} \right\} \\
& = \int{\frac{d\xb d\vb}{(2\pi)^N}
e^{-\frac{1}{2} \ba{cc} \hspace{-1mm} \vb^T, & \hspace{-2mm} \xb^T \hspace{-1mm}\ea
\ba{cc} \hspace{-1mm} \Ib_N & -2a\eta \Ib_N \hspace{-1mm} \\ \hspace{-1mm} -2a\eta \Ib_N & (1-2a^2\eta)\Ib_N \hspace{-1mm} \ea
\ba{c} \hspace{-1mm} \vb \hspace{-1mm} \\ \hspace{-1mm} \xb \hspace{-1mm} \ea }} \\
& = \frac{1}{\mbox{det}^{N/2}
\ba{cc} 1 & -2a\eta \\ -2a\eta & 1-2a^2\eta \ea} = \left(\frac{1}{1-2a^2\eta(1+2\eta)}\right)^{N/2} \ .
\end{align*}
Thus, Lemma \ref{Lem:Gaussian_integral} has hereby been proved.
\qd

\subsection{Proving Lemma \ref{Lem:ML_is_true_sol}}
\label{subsec:ML_proof}
In the following we proof that the ML solution is likely to be the transmitted symbol vector.\\
{\bf Lemma \ref{Lem:ML_is_true_sol}}
\textit{
Let the signal-to-noise ratio be chosen such that $SNR = \eta \ln(N_T)$ where $\eta$ is a constant and define $\varsigma \triangleq N_R/N_T$. For the symbol set with the cardinality $\left|\Omega\right|=2$ we have
\[
{\text{IFF}} \ \ \frac{\varsigma \eta}{2} > 1 , \ \ {\text{then}} \ \ P_{ML} \leq N_T^{-(\varsigma \eta/2-1)},
\] where $P_{ML}$ is the probability of an error in the ML solution.

\vspace{2mm}
\begin{proof}
Define $\tilde{\sb} \triangleq \sb - \sb_{ML}$, where $\sb$ represents the transmitted vector. We can then express $\Hb\tilde{\sb}$ as $\Ss \hs$, by introducing the matrix $\Ss \triangleq {\text{diag}}\left(\tilde{\sb}^T, \ldots, \tilde{\sb}^T \right) \in \Rbb^{N_R \times N_R N_T}$ and letting $\hs \triangleq \vec\left(\Hb\right)$ be a $N_R N_T$-dimensional column vector. Then the probability of making a decision error in the decoded sequence can be expressed as
\begin{equation}
\label{EQ:P_error_ML}
\begin{split}
& P_{EP} \\ &= P\left( \left\| \yb - \sqrt{\frac{SNR}{\sigma_s^2 N_T}}\Hb\sb \right\|^2 \geq \left\| \yb - \sqrt{\frac{SNR}{\sigma_s^2 N_T}}\Hb \sb_{ML} \right\|^2\right) \\
\\ &= P\left( \left\| \upsib \right\|^2 \geq \left\| \yb - \sqrt{\frac{SNR}{\sigma_s^2 N_T}}\Hb \tilde{\sb} \right\|^2\right) \ .
\end{split}
\end{equation}
By applying the Chernoff bound in \eqref{EQ:P_error_ML} and introducing the parameter $0 \leq \kappa \leq 1$, we get the expression given in \eqref{EQ:P_error_ML_Chernoff},
\begin{figure*}[!ht]
\begin{subequations}
\label{EQ:P_error_ML_Chernoff}
\begin{align}
P_{EP} & \leq E\left\{e^{\frac{1}{2}\kappa\left(\left\| \upsib \right\|^2 - \left\| \upsib+\sqrt{\frac{SNR}{\sigma_s^2 N_T}} \Hb\tilde{\sb} \right\|^2 \right)} \right\} = \int{\partial \upsib \partial \hs \frac{e^{-\frac{1}{2}\upsib^T\upsib}}{\sqrt{(2\pi)^{N_R}}} \frac{e^{-\frac{1}{2}\hs^T\hs}}{\sqrt{(2\pi)^{N_R N_T}}} e^{-\frac{1}{2} \kappa \left(\upsib^T\upsib - \left\| \upsib + \sqrt{\frac{SNR}{\sigma_s^2 N_T}}\Ss \hs \right\|^2 \right)} } \\
&=  \int{\frac{\partial \upsib \partial \hs}{\sqrt{(2\pi)^{N_R(N_T+1)}}} e^{-\frac{1}{2}\left[\upsib^T, \hs^T\right] \times \As \times \left[\upsib^T, \hs^T\right]^T} } \label{EQ:Det_P_error_ML} \ ,
\end{align}
\end{subequations}
\end{figure*
where $\As \triangleq \left[ {\begin{array}{*{20}c}
   {{\mathop{\rm \Ib}\nolimits}_{N_R}} & {\kappa \sqrt{\frac{SNR}{\sigma_s^2 N_T}} \Ss}  \\
   {\kappa \sqrt{\frac{SNR}{\sigma_s^2 N_T}} \Ss^T} & {{\mathop{\rm \Ib}\nolimits}_{N_R N_T }  + \kappa \frac{SNR}{\sigma_s^2 N_T} \Ss^T\Ss}  \\
\end{array}} \right]$. If we use the fact that
\[
\int_{-\infty }^\infty{\partial {\bf x} \ e^{-\frac{1}{2}{\bf x}^T{\Sigma}^{-1}{\bf x}}} = \sqrt{(2\pi)^{N_T} \det \left({\Sigma}\right)} \ \ , \Sigma \succ 0 \ ,
\]
and assume that $\As \succ 0$ is positive definite, we can simplify the expression of $P_{EP}$ to
\begin{subequations}
\label{EQ:P_error_ML_simplified}
\begin{align}
P_{EP} & \leq  \det \left(\As \right)^{-1/2} \\
&= \det \left(\Ib_{N_R N_T} + \kappa(1-\kappa) \frac{SNR}{\sigma_s^2 N_T} \Ss^T\Ss  \right) \label{EQ:Schur_compl} \\
&= \det \left(\Ib_{N_R N_T} + \kappa(1-\kappa) \frac{SNR}{\sigma_s^2 N_T} \left\| \tilde{\sb} \right\|^2 \Ib_{N_T} \right)^{-1/2} \\
&=  \left(1 + \kappa(1-\kappa) \frac{SNR}{\sigma_s^2 N_T} \left\| \tilde{\sb} \right\|^2\right)^{-N_R/2} \label{EQ:det_trick} \ .
\end{align}
\end{subequations}
Here we have employed the Schur complement in \eqref{EQ:Schur_compl} and in \eqref{EQ:det_trick} we use  $\det \left(\Ib + \Ab \Bb \right) = \det \left(\Ib + \Bb \Ab \right)$ along with $\Ss \Ss^T = \left\|\tilde{\sb} \right\|^2 \Ib_{N_R}$. Now if we choose $\kappa = 1/2$, which leads to the highest value for \eqref{EQ:P_error_ML_simplified}, we get
\begin{equation}
P_{EP}	\leq \left( 1 + \frac{SNR}{4 \sigma_s^2 N_T} \left\| \tilde{\sb} \right\|^2 \right)^{-N_T/2} \ .
\end{equation}
In order to find the probability that the ML solution is not the transmitted sequence, we sum over all symbol settings in the sequence. For simplicity we assume that the cardinality is $\left|\Omega\right|=2$, which leads to
\begin{subequations}
\begin{align}
P_{ML} &\leq \sum\limits_{i = m}^{N_T}{\binom{N_T}{m} \left( 1 + \frac{SNR}{4 \sigma_s^2 N_T }m \left\| \tilde{\sb} \right\|^2 \right)^{-\varsigma N_T/2}} \\
&=  \sum\limits_{i = m}^{N_T}{\binom{N_T}{m} \left( 1 + \frac{SNR}{2 N_T}m \right)^{-\varsigma N_T/2}} \\ & \approx \sum\limits_{i = m}^{N_T}{\binom{N_T}{m} e^{-\varsigma \cdot SNR \cdot  m/2}} \label{EQ:Approx_P_EP} = \left(1 + e^{-\varsigma \cdot SNR/2} \right)^{N_T} -1 \\
&= \left(1 + e^{-\varsigma \cdot \eta \ln(N_T)/2} \right)^{N_T} -1 \label{EQ:P_EP_second_last} \ ,
\end{align}
\end{subequations}
where the approximation in \eqref{EQ:Approx_P_EP} is valid for large $N_T$. For large $N_T$ we can further simplify the expression in \eqref{EQ:P_EP_second_last} to
\begin{equation}
\begin{split}
P_{ML} &\leq \left(1 + N_T^{-\varsigma \cdot \eta/2} \right)^{N_T} -1  \\ & \approx N_T^{-\left(\varsigma \cdot \eta/2-1\right)}  \ \ {\text{for}} \ \  \varsigma \eta/2 > 1  \label{EQ:P_ML_convergence} \ .
\end{split}
\end{equation}
From \eqref{EQ:P_ML_convergence} we see that the probability of error asymptotically goes to zero as $N_T \rightarrow \infty$ when $\varsigma \eta/2 > 1$.
\end{proof}
\section{Conclusion}
\label{sec:Conclusion}
In this paper we considered solving the integer
least-squares problem using Monte Carlo Markov Chain Gibbs
sampling. The novelty of the proposed MCMC method is that, unlike simulated
annealing techniques, we have a fixed temperature parameter in all the
iterations, with the property that after the Markov chain has mixed,
the probability of encountering the optimal solution is only
polynomial small (i.e. not exponentially small). We further compute
the optimal (here largest) value of the temperature parameter that
guarantees this. Simulation results indicate the
sensitivity of the method to the choice of the temperature parameter
and show that our computed value gives a very good approximation to
its optimal value. Investigating whether the Markov chain mixes in
polynomial time for this choice of temperature parameter is currently
under investigation.
\section{Computing the optimal $\alpha$}
\label{sec:comp_opt_alpha}

Assuming that the vector $\sb = -\oneb$ has been transmitted, the
probability of finding this solution {\em after the Markov chain has
  mixed} is simply $\pi_{-\oneb}$, the steady-state probability of
being in the all $-1$ state. Clearly, if this probability is
exponentially small, it will take exponentially long for the Gibbs
sampler to find it. We will therefore insist that the mean of
$\pi_{-\oneb}$ be only polynomially small.

\input{Finding_optimal_alpha/mean_steady_state.tex}
\input{Finding_optimal_alpha/Value_of_alpha.tex}
\subsection{Mean of $\pi_{-\oneb}$}

This calculation has a lot in common with the one
given in Section \ref{sec:P_error}. Note that the steady state value
of $\pi_{-\oneb}$ is simply
\begin{subequations}
\label{Eq:mean_of_pi}
\begin{align}
\pi_{-\oneb} & = \frac{e^{-\frac{1}{2\alpha^2}\left\|\yb+\sqrt{\frac{\SNR}{N}}\Hb \oneb\right\|^2}}
{\sum_\sb e^{-\frac{1}{2\alpha^2}\left\|\yb+\sqrt{\frac{\SNR}{N}}\Hb \sb\right\|^2}} \\
& = \frac{e^{-\frac{1}{2\alpha^2}\left\|\upsib\right\|^2}}
{\sum_\sb e^{-\frac{1}{2\alpha^2}\left\|\upsib+\sqrt{\frac{\SNR}{N}}\Hb(\sb-\oneb)\right\|^2}} \\
& = \frac{e^{-\frac{1}{2\alpha^2}\left\|\upsib\right\|^2}}
{\sum_{\delb} e^{-\frac{1}{2\alpha^2}\left\|\upsib+2\sqrt{\frac{\SNR}{N}}\Hb \delb\right\|^2}} \\
& = \frac{1} {\sum_{\delb} e^{-\frac{1}{2\alpha^2}\left(
\left\|\upsib+2\sqrt{\frac{\SNR}{N}}\Hb\delb\right\|^2-\|\upsib\|^2\right)}} \ ,
\end{align}
\end{subequations}
where $\delb$ is a vector of zeros and ones and the summations (over
$\sb$ and $\delb$) are over $2^n$ terms.

Now, by Jensen's inequality
\begin{subequations}
\label{Eq:Expetaion_of_pi}
\begin{align}
E \left\{ \pi_{-\oneb} \right\} & \geq \frac{1}{E \left\{ \frac{1}{\pi_{-\oneb}}\right\} } \\
 & =
\frac{1}{E \left\{ \sum_{\delb} e^{-\frac{1}{2\alpha^2}\left(
\left\|\upsib+2\sqrt{\frac{\SNR}{N}}\Hb \delb\right\|^2-\left\|\upsib\right\|^2\right)} \right\}} \\
& = \frac{1}
{\sum_{\delb} E \left\{ e^{-\frac{1}{2\alpha^2}\left(
\left\|\upsib+2\sqrt{\frac{\SNR}{N}}\Hb \delb\right\|^2-\left\|\upsib\right\|^2\right) }\right\} } \\
& = \frac{1}{1+\sum_{\delb \neq 0}
\left(\frac{1}{1+4\frac{\SNR\left\|\delb\right\|^2}{N}
\frac{1}{\alpha^2}(1-\frac{1}{\alpha^2})}\right)^{N/2}} \label{Eq:Jensen_part4} \\
& = \frac{1}{1+\sum_{i=1}^N\left(\begin{array}{c} N \\ i \end{array} \right)
\left(\frac{1}{1+\frac{\beta i}{N}}\right)^{N/2}} \label{Eq:Jensen_part5} \ .
\end{align}
\end{subequations}
In \eqref{Eq:Jensen_part4} we have used Lemma \ref{lem:g-i} and in
 \eqref{Eq:Jensen_part5} we have defined $\beta \triangleq
 4\SNR\frac{1}{\alpha^2}(1-\frac{1}{\alpha^2})$.
 While it is possible to focus on the linear and sublinear terms in the
above summation separately, to give conditions for $E \left\{
 \pi_{-\oneb} \right\}$ to have
the form of $1/\mbox{poly}(N)$, we will be interested in the exact
exponent and so will need a more accurate estimate. To do
this we shall use saddle point integration. Note that
\begin{equation*}
\left(\begin{array}{c} N \\ i \end{array} \right)
\left(\frac{1}{1+\frac{\beta i}{N}}\right)^{N/2} \\
\approx e^{N H(\frac{i}{N})-\frac{N}{2}\ln\left(1+\frac{\beta i}{N}\right)} \ ,
\end{equation*}
where again $H(\cdot)$ represents the entropy in ``nats''. And so the
summation in the denominator of \eqref{Eq:Jensen_part5} can be
approximated as a Stieltjes integral:
\begin{subequations}
\begin{align}
\sum_{i=1}^N\left(\begin{array}{c} N \\ i \end{array} \right)
\left(\frac{1}{1+\frac{\beta i}{N}}\right)^{N/2} & \approx
N\sum_{i=1}^Ne^{N H(\frac{i}{N})-\frac{N}{2}\ln\left(1+\frac{\beta
i}{N}\right)}\frac{1}{N} \\
& \approx N\int_0^1e^{N H(x)-\frac{N}{2}\ln\left(1+\beta x\right)}dx \ .
\end{align}
\end{subequations}
For large $N$, this is a saddle point integral and can be approximated
by the formula
\be
\int_0^1e^{N f(x)}dx \approx \sqrt{\frac{2\pi}{N|f''(x_0)|}}e^{N f(x_0)} \ ,
\label{Eq:saddlepoint}
\ee
where $x_0$, is the saddle point of $f(\cdot)$, i.e.,$f'(x_0) = 0.$
In our case,
\[ f(x) = -x\ln x-(1-x)\ln(1-x)-\frac{1}{2}\ln(1+\beta x) \ , \]
and so
\[ f'(x) = \ln\frac{1-x}{x}-\frac{1}{2}\frac{\beta}{1+\beta x} \ . \]
In general, it is not possible to solve for $f'(x_0) = 0$ in closed
form. However, in our case, if we assume that $\beta = 4\SNR
\frac{1}{\alpha^2}(1-\frac{1}{\alpha^2})\gg 1$ (which is true
since the SNR grows at least logarithmically),
then it is not too hard to verify that the saddle point is given by
\be
x_0 = e^{-\frac{\beta}{2}} \ .
\ee
And hence $f(x_0) = $
\begin{equation*}
\begin{split}
& -e^{-\frac{\beta}{2}}\ln e^{-\frac{\beta}{2}}
-(1-e^{-\frac{\beta}{2}})\ln(1-e^{-\frac{\beta}{2}})
- \frac{1}{2}\ln(1+\beta e^{-\frac{\beta}{2}}) \\
& \approx
\frac{\beta}{2}e^{-\frac{\beta}{2}}+e^{-\frac{\beta}{2}}-\frac{1}{2}
\beta e^{-\frac{\beta}{2}}
= e^{-\frac{\beta}{2}} \ ,
\end{split}
\end{equation*}
and further plugging $x_0$ into $f''(x) = -\frac{1}{x}
-\frac{1}{1-x}-\frac{1}{2}\frac{\beta^2}{(1+\beta x)^2}$, yields
\be
f''(x_0) \approx -e^{\frac{\beta}{2}}-1+\frac{1}{2}\beta^2 \approx
-e^{\frac{\beta}{2}} \ .
\ee
Replacing these into the saddle point expression in \eqref{Eq:saddlepoint} show that
\begin{equation}
\label{Eq:sum_approx_by_saddl}
\sum_{i=1}^N \left(\begin{array}{c} N \\ i \end{array} \right)
\left(\frac{1}{1+\frac{\beta i}{N}}\right)^{N/2} \approx
\sqrt{2\pi/N} \exp{\left(N e^{-\frac{\beta}{2}}-\frac{\beta}{4}\right)} \ .
\end{equation}
We want $E \left\{ \pi_{-\oneb} \right\}$ to behave as $\frac{1}{N^\zeta}$ and according to \eqref{Eq:Expetaion_of_pi} this means
that we want the expression in \eqref{Eq:sum_approx_by_saddl} to behave as $N^{\zeta}$. Let us take
\[ e^{Ne^{-\frac{\beta}{2}}} = N^{\zeta} \ . \]
Solving for $\beta$ yields
\be
\beta = 4\SNR \frac{1}{\alpha^2}\left(1-\frac{1}{\alpha^2}\right) =
2\left(\ln N -\ln\ln N -\ln\zeta \right) .
\ee
Incidentally, this choice of $\beta$ yields $e^{-\frac{\beta}{4}}
\approx \frac{1}{\sqrt{N}}$,
and so we have the following result.

\begin{lemma}[Mean of $\pi_{-\oneb}$] If $\alpha$ is chosen such that
\be
\label{EQ:Alpha_expression}
\frac{\alpha^2}{1-\frac{1}{\alpha^2}} = \frac{2\SNR}
{\ln N -\ln\ln N -\ln\zeta} \ ,
\ee
then
\be
\label{Eq:Mean_pi_lemma}
E \left\{\pi_{-\oneb} \right\} \geq N^{-\zeta} \ .
\ee
\end{lemma}
\subsection{Value of $\alpha$}

Note that from (\ref{Eq:Jensen_part5}) it is clear that the larger
$\beta$ is, the larger $\pi_{-\oneb}$ is. Therefore, the range of
$\alpha$ that gives a polynomially small probability to $\pi_{-\oneb}$
is
\begin{equation}
\frac{\alpha^2}{1-\frac{1}{\alpha^2}} \geq \frac{2\SNR}
{\ln N -\ln\ln N -\ln\zeta}.
\end{equation}
It can be shown that in the regime, $\SNR>2\ln N$, the above quadratic
inequality in $\alpha$ has two positive real solutions, $\alpha_+\geq
\alpha_-$, and that the inequality holds for all
$\alpha\in[\alpha_-,\alpha_+]$.

We know that, the larger $\alpha$ is, the faster the Markov chain
mixes.\footnote{In general, there is a trade-off between
faster mixing time of the Markov chain (due to an increase of
$\alpha$) versus slower encountering the optimal solution in
steady-state. In fact, at infinite temperature our algorithm reduces
to a random walk in a hypercube which mixes in $O(N\ln N)$ time.}
Therefore it is reasonable that we choose the largest
permissible value for $\alpha$, i.e., $\alpha_+$.

Figures \ref{fig:alpha_vs_SNR_N=10} and
\ref{fig:alpha_vs_SNR_N=50} show the values of $\alpha_+$
and $\alpha_-$ as a function of $\SNR$ for systems with $N=10$ and $N=50$, when we have $\zeta = 1/\ln N$.
\begin{figure}[btp]
 \center
 \includegraphics[width=2.55in]{Figures/Value_of_alpha_vs_SNR_for_N=10_zeta=logN-1.eps}
 \vspace{-2mm}
\caption{Value of $\alpha$ vs.~$\SNR$ for system size $N=10$.}
\label{fig:alpha_vs_SNR_N=10}
\vspace{-2mm}
\end{figure}

\begin{figure}[htbp]
 \center
 \includegraphics[width=2.55in]{Figures/Value_of_alpha_vs_SNR_for_N=50_zeta=logN-1.eps}
 \vspace{-2mm}
\caption{Value of $\alpha$ vs.~$\SNR$ for system size $N=50$.}
\label{fig:alpha_vs_SNR_N=50}
\vspace{-2mm}
\end{figure}

\subsection{Mixing time of Markov Chain}
One open question is whether the Markov chain is rapidly mixing when
using the strategy above for choosing $\alpha$. This
is something we are currently investigating, and the simulations
presented in Section \ref{sec:sim_results} seem to indicate that this
is the case. Furthermore, the
simulations also suggest that the computed value of $\alpha$ is very
close to the optimal choice, even in the case where the condition
$\SNR>2\ln(N)$ is not satisfied.
\section{Gibbs Sampling}
\label{sec:Gibbs_sampling}
One way of solving the optimization problem given in
\eqref{EQ:Original_minimization_problem} is by using Markov Chain
Monte Carlo (MCMC) simulations, which asymptotically converge to the
optimal solution \cite{Mackay_03}. More specifically, the MCMC
detector we investigate
here is the Gibbs sampler, which computes the conditional probability
of each symbol in the constellation set at the $j$th index in the
estimated symbol vector. This conditional probability is obtained by
keeping the $j-1$ other values in the estimated symbol vector
fixed. Thus, in $k$th iteration the probability of the $j$th symbol
adopts the value $\omega$, is given as
\begin{equation}
\label{Eq:Prob_of_symbol_MCMC}
p\left( {\hat{\sb}_j^{(k)} = \omega \left|{ \theta }\right.} \right) =
\frac{e^{-\frac{1}{2\alpha^2} \left\| \yb - \sqrt{\frac{\SNR}{N}} \Hb
    \tilde{\sb}_{j \left|{\omega}\right.} \right\|^2   }}{
  \sum\limits_{\tilde{\sb}_{j \left|{\tilde{\omega}}\right.} \in
    \Omega}{e^{-\frac{1}{2\alpha^2} \left\| \yb -
      \sqrt{\frac{\SNR}{N}} \Hb \tilde{\sb}_{j \left|{ \tilde{\omega}
	}\right.} \right\|^2 } }}  \ ,
\end{equation}
where $\tilde{\sb}_{j \left|{\omega}\right. }^T \triangleq
\left[\hat{\sb}_{1:j-1}^{(k)}, \omega, \hat{\sb}_{j+1:N_T}^{(k-1)}
  \right]^T$ and where we for simplicity have introduced $\theta =
\left\{ \hat{\sb}^{(k-1)}, \yb, \Hb \right\}$.\footnote{When we
  compute the probability of symbol $\omega$ at the $j$'th position,
  we more precisely condition on the symbols $\hat{\sb}_{1:j-1}^{(k)}$
  and $\hat{\sb}_{j+1:N_T}^{(k-1)}$, but to keep the notation simple,
  we do not explicitly state that in the equations above.} $\alpha$
represents a tunable positive parameter which controls the mixing time
of the Markov chain, this parameter is also sometimes called the
"temperature". The  larger $\alpha$ is the faster the mixing time of
the Markov chain will be, but as we will show in the paper, there is
an upper limit on $\alpha$, in order to ensure that the probability of
finding the optimal solution in steady state is not exponentially
small. The MCMC method will with probability $p\left(
{\hat{\sb}_j^{(k)} = \omega \left|{\theta}\right.} \right)$ keep
$\omega$ at the $j$'th index in estimated symbol vector, and compute
conditional probability the $(j+1)$th index in a similar fashion. We
define one iteration of the Gibbs sampler as a randomly-ordered update of
all the $j = \left\{1, \ldots, N_T \right\}$ indices in the estimated
symbol vector $\hat{\sb}$.\footnote{We need a randomly-ordered update
  for the Markov chain to be reversible and for our subsequent
  analysis to go through. It is also possible to just randomly select
  a symbol $j$ to update, without insisting that a full sequence be
  done. This also makes the Markov chain reversible and has the same
  steady state distribution. In practice a fixed, say sequential,
  order can be employed, although the Markov chain is no longer
  reversible. Note that our theoretical analysis is assuming randomly selected
symbol updates for analytical convenience. In our experimental
section we used a sequential updating order which empirically yields a slight
convergence acceleration.} The initialization of the symbol vector
$\hat{\sb}^{(0)}$ can either be chosen randomly or, alternatively,
e.g. the zero-forcing solution can be used.

\subsection{Complexity of the Gibbs sampler}
\label{subsec:Gibbs_complexity}
The conditional probability for the $j$'th symbol in \eqref{Eq:Prob_of_symbol_MCMC} can be computed efficiently by reusing the result obtained for the $j-1$'th symbol, when we evaluate $\left\| \yb - \sqrt{\SNR/N} \Hb \tilde{\sb}_{j \left|{\omega}\right.} \right\|^2$. Since we are only changing the $j$'th symbol in the symbol vector, the difference $\db_{j} \triangleq \yb - \sqrt{\SNR/N} \Hb \tilde{\sb}_{j \left|{\omega }\right.} $ can be expressed as
\begin{equation}
\label{EQ:difference_for_norm}
 \db_j = \db_{j-1} - \sqrt{\frac{\SNR}{N}} \Hb_{1:N,j} \Delta s_{j\left|{\omega}\right.} \ ,
\end{equation}
where $\Delta s_{j\left|{\omega}\right.} \triangleq s_{j \left|{\omega}\right.}^{(k)} - s_{j \left|{ \tilde{\omega} }\right.}^{(k-1)}$.  Thus, the computation of conditional probability of certain symbol in the $j$'th position costs $2N$ operations, where we define an operation as a Multiply and Accumulate (MAC) instruction.\footnote{We need to compute both the inner product $\db_j^T \db_j$ and the product $\Hb_{1:N,j} \Delta s_{j\left|{\omega}\right.}$.} This leads to a complexity of $\bigO \left( 2N^2[\left|\Omega \right| -1 ]\right)$ operations per iteration. For further details on the implementation of the Gibbs sampler see \cite{Laraway_Farhang-Boroujeny_IEEE_09}.

\section{Introduction}
\label{sec:Introduction}
The problem of performing Maximum Likelihood (ML) decoding in digital
communication has gained much attention over the years. One method to
obtain the ML solution is Sphere Decoding (SD)
\cite{Hochwald_Ten-Brink_03, Hassibi_1, Hassibi_2,Agrell_et_al_02,
  Damen_et_al}. Over a wide range of Signal-to-Noise Ratios ($\SNR$)s
the average complexity of SD is significantly smaller than exhaustive
search detectors, but in worst case the complexity is still
exponential \cite{Ottersten_05}. Thus, in scenarios with poor $\SNR$
or in Multiple-Input Multiple-Output (MIMO) systems with huge transmit
and receive dimensions, even SD can be infeasible. A way to overcome
this problem is to use approximate Markov Chain Monte Carlo (MCMC)
detectors instead, which asymptotically can provide the optimal
solution, \cite{Robert_MC_Stat_methods_04, Haggstrom_02}. Gibbs
sampling (also known as Glauber dynamics) is one MCMC method, which is
used for sampling from distributions of multiple dimensions. The Gibbs
sampler has among others been proposed for detection purposes in wireless
communication in \cite{Zhu_Farhang_Boroujeny_05, Farhang_Boroujeny_06, Wang_Poor_03, Chen_Wang_2002} (see also the references therein). The scope of this
paper is to describe and analyse a new way of solving the integer
least-squares problem using MCMC. It will be shown that the method can
be used for achieving a near-optimal and computationally efficient
solution of the problem, even for systems having a huge dimension.

The paper is organized as follows; In Section \ref{sec:System_model}
we present the system model that will be used throughout the
paper. The MCMC method is described in Section
\ref{sec:Gibbs_sampling} and in Section \ref{sec:P_error} we analyse
the probability of error for the ML detector. Section
\ref{sec:comp_opt_alpha} treats the optimal selection of the
temperature parameter $\alpha$, while the simulation results are given
in Section \ref{sec:sim_results} and some concluding remarks are found
in Section \ref{sec:Conclusion}.
\section{Probability of Error}
\label{sec:P_error}

In this paper, we are interested in evaluating the performance of the
aforementioned Gibbs sampler, compared to the ML solution. To ease our
analysis, we will assume that the ML detector finds the correct
transmitted vector. Before we derive the probability of error for the
ML detector, we will state a lemma which we will make repeated use of.
\begin{lemma}[Gaussian Integral] \label{Lem:Gaussian_integral} Let $\vb$ and $\xb$ be independent
  Gaussian random vectors with distribution ${\cal N}(\zerob,\Ib_N)$
  each. Then, if $1-2a^2\eta(1+2\eta)>0$,
\be
E \left\{ e^{\eta\left(\|\vb+a\xb\|^2-\|\vb\|^2\right)} \right\}=
  \left(\frac{1}{1-2a^2\eta(1+2\eta)}\right)^{N/2}.
\ee
\label{lem:g-i}
\end{lemma}
\begin{proof}
\label{Pro:Gaussian_integral}
See Appendix \ref{subsec:Gaussian_integral} for a detailed proof.
\end{proof}
\vspace{2mm}
Assuming that the vector $\sb= -\oneb$ was transmitted, the ML
detector will make an error if there exists a vector $\sb\neq -\oneb$
such that
\[
\left\|\yb-\sqrt{\frac{\SNR}{N}}\Hb\sb\right\|^2\leq
\left\|\yb+\sqrt{\frac{\SNR}{N}} \Hb\oneb\right\|^2 = \|\upsib\|^2 \ .
\] In other words,
\begin{eqnarray*}
P_e & = & \mbox{Prob}\left(\left\|\yb-\sqrt{\frac{\SNR}{N}}\Hb\sb\right\|^2\leq
  \|\upsib\|^2 \right) \\
& = & \mbox{Prob}\left(\left\|\upsib+\sqrt{\frac{\SNR}{N}}\Hb(-\oneb-\sb)\right\|^2\leq
  \|\upsib\|^2 \right) \ ,\\
\end{eqnarray*}
for some $\sb\neq -\oneb$, which can be formulated as
\begin{eqnarray*}
P_e & = &  \mbox{Prob}\left(\left\|\upsib+2\sqrt{\frac{\SNR}{N}}\Hb\delb\right\|^2\leq
  \|\upsib\|^2 \right) \
\end{eqnarray*}
for some $\delb\neq 0$. Note that in the above equation $\delb$ is a vector of zeros and
$-1$'s. Now using the union bound
\be
P_e \leq \sum_{\delb\neq 0}
\mbox{Prob}\left(\left\|\upsib+2\sqrt{\frac{\SNR}{N}}\Hb\delb\right\|^2\leq
  \|\upsib\|^2\right).
\ee
We will use the Chernoff bound to bound the quantity inside the
summation. Thus,
\begin{subequations}
\begin{align}
& \mbox{Prob}\left(\left\|\upsib+2\sqrt{\frac{\SNR}{N}}\Hb\delb\right\|^2 \leq \|\upsib\|^2\right) \\
& \leq E \left\{ e^{-\beta  \left(\left\|\upsib+2\sqrt{\frac{\SNR}{N}}\Hb\delb\right\|^2-\|\upsib\|^2\right)} \right\} \\
& = \left(\frac{1}{1+8\frac{\SNR\|\delb\|^2}{N} \beta(1-2\beta)}\right)^{N/2},
\end{align}
\end{subequations}
where $\beta\geq 0$ is the Chernoff parameter, and where we have used
Lemma \ref{lem:g-i} with $\eta = -\beta$ and
$a = 2\sqrt{\frac{\SNR\|\delb\|^2}{N}}$, since
\[ E \left\{ \left(2\sqrt{\frac{\SNR}{N}}\Hb\delb\right)
\left(2\sqrt{\frac{\SNR}{N}}\Hb\delb\right)^* \right\} =
4\frac{\SNR\|\delb\|^2}{N} \Ib_N. \]
The optimal value for $\beta$ is $\frac{1}{4}$, which yields the
tightest bound
\be
\mbox{Prob}\left(\left\|\upsib+2\sqrt{\frac{\SNR}{N}}\Hb\delb\right\|^2\leq
  \|\upsib\|^2\right) \leq \left(\frac{1}{1+\frac{\SNR\|\delb\|^2}{N}}
\right)^{N/2}.
\ee
Note that this depends only on $\|\delb\|^2$, the number of nonzero
entries in $\delb$. Plugging this into the union bound yields
\be
P_e \leq \sum_{i=1}^N \left( \begin{array}{c} N \\ i \end{array}
\right) \left(\frac{1}{1+\frac{\SNR i}{N}}
\right)^{N/2}.
\ee

Let us first look at the linear (i.e., $i$ proportional to $N$) terms
in the above sum. Thus,
\[ \left( \begin{array}{c} N \\ i \end{array}
\right) \left(\frac{1}{1+\frac{\SNR i}{N}}
\right)^{N/2} \approx
e^{N H(\frac{i}{N})-\frac{N}{2}\ln\left(1+\frac{\SNR i}{N}\right)}, \]
where $H(\cdot)$ is entropy in ``nats''. Clearly, if
$\lim_{N\rightarrow\infty}\SNR = \infty$, then the linear terms go to
zero (superexponentially fast).

Let us now look at the sublinear terms. In particular, let is look at
$i=1$:
\[ N\left(\frac{1}{1+\frac{\SNR}{N}}\right)^{N/2} \approx
N e^{-\SNR/2}. \]
Clearly, to have this term go to zero, we require that $\SNR>
2\ln N$. A similar argument shows that all other sublinear terms also go to
zero, and so.\footnote{Due to space constraints we only present a sketch of this bound. A
rigorous proof can be given using the saddle point method, similarly
to the proof in the next section.}

\begin{lemma}[SNR scaling] If $\SNR>2\ln N$, then
  $P_e\rightarrow 0$ as $N\rightarrow\infty$.
\end{lemma}

\section{Simulation Results}
\label{sec:sim_results}
\begin{figure}[tp]
	\centering
	\includegraphics[width=2.6in]{Figures/sim_MCMC_BER_vs_iter_Alphabet=ChType=RFS_N=10_SNRdB=10_MinErr=500.eps}
	\vspace{-2mm}
	\caption{BER vs. iterations, $10 \times 10$. $\SNR$ = 10 dB.}
	\label{fig:Sim_alpha_SNR=10}
	\vspace{-2mm}
\end{figure}
\begin{figure}[tp]
	\centering
  \includegraphics[width=2.6in]{Figures/sim_MCMC_BER_vs_iter_Alphabet=ChType=RFS_N=10_SNRdB=14_MinErr=500.eps}
	\vspace{-2mm}
	\caption{BER vs. iterations, $10 \times 10$ system. $\SNR$ = 14 dB.}
	\label{fig:Sim_alpha_SNR=14}
	\vspace{-2mm}
\end{figure}
In this section we present simulation results for a MIMO $N \times N$
system with a full square channel matrix containing i.i.d.~Gaussian
entries. In Fig. \ref{fig:Sim_alpha_SNR=10} and Fig.
\ref{fig:Sim_alpha_SNR=14} the Bit Error Rate (BER) of the Gibbs
sampler, initialized with a random $\sb$, has been evaluated as a
function of the number of iterations
in a $10 \times 10$ system using a variety of $\alpha$ values. Thereby,
we can inspect how the parameter $\alpha$ affects the convergence rate
of the Gibbs sampler.
The performance of the Maximum Likelihood (ML), the Zero-Forcing (ZF),
and the Linear Minimum Mean Square Error (LMMSE) detector has also
been plotted, to ease the comparison of the Gibbs sampler with
these. It is seen that the Gibbs sampler outperforms both the ZF and
the LMMSE detector after only a few iterations in all the presented
simulations, when the tuning parameter $\alpha$ is chosen
properly. Furthermore, it is observed that the parameter $\alpha$ has
a huge influence on the convergence rate and that the Gibbs sampler
converges toward the ML solution as a function of the
iterations.\footnote{It should be noted that the way we decode the
  symbol vector to a given iteration, is to select the symbol vector
  which has the lowest cost function in all the iterations up to that
  point in time.} The optimal value of $\alpha$ (in terms of
convergence rate) is quite close to the theoretical values from Fig. \ref{fig:alpha_vs_SNR_N=10} of $\alpha_+ =
2.7$ and $\alpha_+ = 4.6$ at $\SNR$'s at $10$ and $14 dB$, respectively. It is also observed that the performance of the Gibbs sampler is significantly deteriorated if the temperature parameter is chosen based on the $\SNR$ (and thereby on the noise variance), such that $\alpha = \sigma \triangleq 1/\SNR$. Thus, the latter strategy is clearly not a wise choice.\\
Figure \ref{fig:Sim_alpha_BER_vs_SNR_iter=100} shows the BER
performance for the MCMC detector for fixed number of iterations, $k =
100$. From the figure we see that the $\SNR$ has a significant
influence on the optimal choice of $\alpha$ given a fixed number of
iterations.
\begin{figure}[tp]
	\centering
\includegraphics[width=2.6in]{Figures/sim_MCMC_BER_vs_SNR_Alphabet=ChType=RFS_N=10_iter=100_MinErr=500_BER.eps}
\vspace{-2mm}
	\caption{BER vs. $\SNR$, $10 \times 10$. Number of iterations, $k = 100$.}
	\label{fig:Sim_alpha_BER_vs_SNR_iter=100}
	\vspace{-2mm}
\end{figure}
\\The performance of the Gibbs sampler is also shown for a
$50 \times 50$ system, which represents a ML decoding problem of huge
complexity where an exhaustive search would require $2^{50}
\approx 10^{15}$ evaluations. For this problem even the sphere decoder
has an enormous complexity under moderate $\SNR$.\footnote{In fact, it
  can be shown that, for $\SNR = \bigO(\ln N)$, the lower bound on the
  complexity of the sphere decoder obtained in \cite{Ottersten_05}
  is exponential.} Therefore, it has not been
possible to simulate the performance of this decoder within a
reasonable time and we have therefore ``cheated'' a little by
initializing the radius of the sphere to the minimum of either the
norm of the transmitted symbol vector or the solution found by the
Gibbs sampler. This has been done in order to evaluate the BER
performance of the optimal detector. Figure
\ref{fig:Sim_alpha_N=50_SNR=12} shows the BER curve as a function of
the iteration number, while Figure
\ref{fig:Sim_alpha_BER_vs_SNR_N=50_iter=500} illustrates the BER curve
vs. the $\SNR$. From Figure \ref{fig:Sim_alpha_N=50_SNR=12} we see
that there is a quite good correspondence between the simulated
$\alpha$ and the theoretical value $\alpha_+ = 2.6$ obtained from
Figure \ref{fig:alpha_vs_SNR_N=50}.
\begin{figure}[tp]
	\centering
  \includegraphics[width=2.6in]{Figures/sim_MCMC_BER_vs_iter_Alphabet=ChType=RFS_N=50_SNRdB=12_MinErr=500.eps}
	\vspace{-2mm}
	\caption{BER vs. iterations, $50 \times 50$ system. $\SNR$ = 12 dB.}
	\label{fig:Sim_alpha_N=50_SNR=12}
	\vspace{-2mm}
\end{figure}
\begin{figure}[tb]
	\centering
\includegraphics[width=2.6in]{Figures/sim_MCMC_BER_vs_SNR_Alphabet=ChType=RFS_N=50_iter=500_MinErr=500_BER.eps}
\vspace{-2mm}
	\caption{BER vs. \SNR, $50 \times 50$ system. Num. of iter., $k = 500$.}
	\label{fig:Sim_alpha_BER_vs_SNR_N=50_iter=500}
	\vspace{-2mm}
\end{figure}
\input{Simulations/Table_of_complexity.tex}
The average complexity (MAC pr. symbol vector) of the Gibbs sampler having a BER performance comparable with the ML detector is shown in Table \ref{Tab:Complexity_SD_vs_GS}. The SD has been included as a reference.\footnote{It has not been possible to simulate the SD for a $50\times50$ system when $SNR\leq10dB$ and, therefore, the complexity of $SNR=12 dB$ has been used a lower bound.} It is observed that the complexity of the Gibbs sampler is not affected by the $\SNR$ as much as the SD.

\section{System Model}
\label{sec:System_model}
We consider a real-valued block-fading MIMO antenna system, with $N$
transmit and $N$ receive dimensions, with know channel
coefficients.\footnote{For simplicity we have assumed that the receive and the transmit dimensions are the same, but the results presented in the paper can be generalized to cover different dimensions.} The received signal $\yb \in \Rbb^N$ can be expressed
as
\begin{equation}
\label{EQ:sig_model_matrix}
\yb = \sqrt{\frac{\SNR}{N}}{\Hb\sb} + \upsib \ ,
\end{equation}
where $\sb \in \Omega^{N}$ is the transmitted signal, and $\Omega$
denotes the constellation set. To simplify the derivations in the
paper we will assume that $\Omega = \left\{\pm 1\right\}$. $\upsib \in
\Rbb^{N}$ is the noise vector where each entry is Gaussian $\Nc
\left(0,1\right)$ and independent identically distributed (i.i.d.),
and $\Hb \in \Rbb^{N \times N}$ denotes the channel matrix with
i.i.d. $\Nc \left(0,1\right)$ entries. The normalization in
(\ref{EQ:sig_model_matrix}) guarantees that $\SNR$ represents the
signal-to-noise ratio per receive dimension (which we define as the ratio of the total transmit energy per channel use divided by the per-component noise variance as described in among others \cite{Damen_et_al}). As explained further below, for analysis
purposes we will focus on the regime where
$\SNR > 2\ln(N)$, in order to get the probability of error of the ML
detector to go to zero. Further, in our analysis, without loss of
generality, we will assume that the all minus one vector was
transmitted, $\sb = -\oneb$. Therefore
\begin{equation}
\yb = \upsib-\sqrt{\frac{\SNR}{N}}\Hb\oneb \ .
\end{equation}

We are considering a minimization of the average error probability
$P\left({\bf e} \right) \triangleq P\left(\hat{\sb} \neq \sb \right)$,
which is obtained by performing Maximum Likelihood Sequence Detection
(here simply referred to as ML detection) given by
\begin{equation}
\label{EQ:Original_minimization_problem}
 \hat{\sb} = \arg	\mathop {\text{min} }\limits_{\sb \in \Omega^{N}} \ \  \left\| \yb - \sqrt{\frac{\SNR}{N}}\Hb \sb \right\|^2 \ .
\end{equation}

redpajama_set_name: RedPajamaArXiv


text:
Updated October 5, 2021
Mechanic Falls council supports keeping local police department
Chief Jeffrey Goss said he expects to hire a patrol sergeant soon.
By Eriks PetersonsSpecial to the Sun Journal
MECHANIC FALLS —The Town Council unanimously adopted a resolution Monday night "offering a united vote of confidence and support to keep and maintain our own local Mechanic Falls Police Department."
Since late summer, the department has had only Chief Jeffery Goss. The town is in the process of hiring a patrol sergeant and three additional patrol officers.
The Androscoggin County Sheriff's Office has assisted with calls when Goss is not on duty.
Goss said previously that the county "can help temporarily but it's not sustainable," adding it will take time for the department to get back to full strength.
He said he has interviewed two people for the sergeant's position and will be able to make a decision soon. The resolution will help attract personnel and he thanked the council for the vote of confidence.
In other matters, the town is also looking to hire a town clerk to replace Julie Ward, who will begin working for Otisfield after Oct. 22. Ward has been town clerk since June 2019.
In other business, the council approved a warrant article for a Nov. 2 vote asking approval to spend $20,694 from the undesignated fund balance "to grant abatements necessary due to clerical errors." The amount is above the limit the council is allowed to approve.
Councilors also appointed Alyssa Morrison to the Regional School Unit 16 board of directors to succeed Arleena Stotts, who resigned in August.
Carrie Paradis was appointed to the Recreation Committee.
Town Manager Vic Hodgkins said the town will receive two installments of $157,000 from the American Rescue Plan Act, the first one this year and the second in 2022. He said the town has until the end of 2024 to inform the federal government how it plans to spend the money and until 2026 to use it.
mechanic falls maine

redpajama_set_name: RedPajamaCommonCrawl


text:
import React from 'react';
import PropTypes from 'prop-types';
import Form from 'react-bootstrap/lib/Form';
import FormGroup from 'react-bootstrap/lib/FormGroup';
import Col from 'react-bootstrap/lib/Col';
import FormControl from 'react-bootstrap/lib/FormControl';
import ControlLabel from 'react-bootstrap/lib/ControlLabel';
import Button from 'react-bootstrap/lib/Button';
import Panel from 'react-bootstrap/lib/Panel';
import Collapse from 'react-bootstrap/lib/Collapse';
import FontAwesome from 'react-fontawesome';
import CSSModules from 'react-css-modules';

import * as FormFactory from '../form/factory.js';
import { SUPPORTED_LANGUAGES } from '../../../config-public.js';

export default class ArticleForm extends React.Component {

  static USER_ROLES = ['FREE', 'USER', 'ADMIN'];

  static propTypes = FormFactory.getFormPropTypes()
  static defaultProps = FormFactory.getFormDefaultPropTypes()

  state = {
    record: this.props.record
  }

  isInvalid = () => {
    const { record } = this.state;
    return !(record.email
      && record.role
      && record.lang
    );
  }

  onSaveClicked = (e) => {
    e.preventDefault();
    this.props.onSave(this.state.record);
  }

  onDeleteClicked = (e) => {
    e.preventDefault();
    this.props.onDelete(this.state.record);
  }

  render () {
    const { isNew } = this.props;
    const { record } = this.state;

    return (
      <Form horizontal>

        { !isNew && FormFactory.createStaticText(record._id, 'ID') }

        { FormFactory.createInput({
          name: 'email',
          label: 'Email',
          type: 'email',
          value: record.email,
          onChange: FormFactory.handleInputChange(this),
          required: true
        }) }

        { FormFactory.createInputDate({
          name: 'lastLogin',
          label: 'Last login',
          value: record.lastLogin,
          onChange: FormFactory.handleDateInputChange(this, 'lastLogin'),
          required: true
        }) }

        { FormFactory.createInput({
          name: 'totalLogins',
          label: 'Total logins',
          type: 'number',
          value: record.totalLogins,
          onChange: FormFactory.handleInputChange(this),
          required: true
        }) }

        { !isNew && FormFactory.createStaticText(record.totalBookmarks, 'Bookmarks') }

        { !record.isEmailValid && FormFactory.createInputDate({
          name: 'validationExpiresAt',
          label: 'Account expires',
          value: record.validationExpiresAt,
          onChange: FormFactory.handleDateInputChange(this, 'validationExpiresAt')
        }) }

        { record.isEmailValid && FormFactory.createStaticText(
          <FontAwesome className='text-success' name="check" />,
          'Account validation'
        ) }

        { FormFactory.createSelection({
          name: 'role',
          value: record.role,
          onChange: FormFactory.handleInputChange(this),
          enumeration: ArticleForm.USER_ROLES,
          required: true
        }) }

        { FormFactory.createSelection({
          name: 'lang',
          value: record.lang,
          onChange: FormFactory.handleInputChange(this),
          enumeration: SUPPORTED_LANGUAGES,
          required: true
        }) }

        { FormFactory.createFormOptionsPanel({
          onDelete: !isNew && this.onDeleteClicked,
          onSave: this.onSaveClicked,
          isInvalid: this.isInvalid(),
          isNew
        }) }

      </Form>
    )
  }

}

redpajama_set_name: RedPajamaGithub


text:
Home Latest News Saudi Bride died in a car crash on the way to her...
Saudi Bride died in a car crash on the way to her wedding ceremony
Car accidents are considered one of the major causes of deaths in Saudi Arabia. According to the recent statistics, a car accident happens every minute on average in Saudi Arabia. More than 7,000 people lose their lives in more than 460,000 car accidents every year.
The reasons behind these accidents are drivers driving at a very fast speed and some of them just doze off. Saudi Arabia is known to have world's longest and best road infrastructure. The roads are wide and invite the drivers to speed up.
With cities located far away and fast vehicles available, the risk is always present. Recently an 18-year-old bride faced a tragic accident on her way to her wedding. How happy the moment might be for her, but unfortunately life had some other plans for her and her family.
It was reported in Riyadh newspaper that the bride died along with several family members after their vehicle crashed. The accident took place in Al Mahd governorate on Monday.
Spokesman of Saudi Red Crescent Khaled Al Sahli said when they received a call reporting that accident, a team of first responders arrived at the place of the accident and noticed that there were four victims 2 already dead and another 2 who were seriously injured.
They were immediately transported to nearby hospitals for treatment. Everybody was shocked and felt sad on hearing this news. This news went viral on social media and the people prayed to Allah to have mercy on their soul. This was indeed a heartbreaking news for everyone.
The National Highways have every kind of vehicles running on them. Trailers, trucks, cars, wagons and what not. The driving there seems to be easy thus the drivers sometimes relax and lose control of the vehicle resulting in fatal and deadly accidents because the speed is too much to handle.
Such accidents should be and can be avoided, for many precious lives are lost. Every life is precious. There might not be a person who has not suffered from these accidents in Saudi Arabia in one way or the other. I lost my school friend in a tragic crash back in 2012 near Jeddah.
The Saudi government is trying to improve traffic management system. They are trying to improve everything by applying Kingdom's Traffic management system Saher.
Saher system is an automated traffic control system in Saudi Arabia. It is a well-equipped online monitoring system linked with national information center of the ministry of interior, it strongly checks the traffic flow through a satellite system.
After the introduction of Saher system the traffic accidents injuries have reduced by 20% and death caused by traffic accidents rate has decreased by 37.8 %.
The Saher system is still working to contribute to lowering the rate of traffic accidents. And it has already improved a lot. in 2016, some nine thousand people lost their lives in traffic accidents and this rate decreased in 2017.
Source: Al Riyadh
12 years jail to Saudi wife, expat husband – bank transfer
Dammam Airport announces new baggage policy
Saudi man, 7-year-old son die of thirst in Saudi desert
Indian man's son died 2 days after coming to KSA
Saudi daughter dies 10 hours after father's death
Imam University launches bachelor's degree in Cinema


text:
Q: Hammerstein stochastic integral equation I'm in trouble with the following integral equation:
$$\phi(t)=\rho\int_0^1 t^2 s \phi(s)^2 ds+\nu(t)$$
where $\nu(t)$ is a white gaussian noise with variance $\sigma$ and mean value $\mu$.
Is it possible to solve this equation in a closed form? Alternatively, can you obtain some property of the spectrum of $\phi(t)$ without solve it?
Thanks for any suggestion

A: Let $\phi$ denote any solution. Then $\phi(t)=\rho t^2X+\nu(t)$ where $X=\int\limits_0^1s\phi(s)^2\mathrm ds$, hence
$$
X=\int\limits_0^1s(\rho s^2X+\nu(s))^2\mathrm ds=\int\limits_0^1(\rho^2 s^5X^2+2\rho s^3X\nu(s)+s\nu(s)^2)\mathrm ds.
$$
One sees that $X=\tfrac16\rho^2X^2+2\rho XY+Z$,
with
$$Y=\int\limits_0^1s^3\nu(s)\mathrm ds,\qquad Z=\int\limits_0^1s\nu(s)^2\mathrm ds.
$$
Thus $X$ is a root of a quadratic polynomial with (random) discriminant proportional to
$$
D=3(2\rho Y-1)^2-2\rho^2Z.
$$
Unless a reason I fail to see ensures that $D\geqslant0$ with full probability, it seems no solution $\phi$ exists.

redpajama_set_name: RedPajamaStackExchange


Hasbro has released a new Darth Tater, the Star Wars' Darth Vader inspired Mr. Potato Head, for 2012. Originally, it seemed like it was going to be a reissue of the original figure. However, new photos have surfaced from Toys "R" Us that show it isn't quite the same figure. The figure sports an entirely new set of accessories including a new helmet, new arms and new shoes.
Click the headline of the story to check out the pics, as well as a comparison I put together.
Apparently they're doing that to a lot their releases. The other day I saw new versions of Mr. and Mrs. with the tag line on the package saying they've "sprouted legs!" The rest of the redesign for them seems to be a cross between the classic look and the Toy Story versions. Of course, if Mrs. came with a set of "Angry Eyes" I would have totally bought it right then and there.
As for the Darth Tater II, I might pick him up, all the same. I gave my original to my kids a few weeks ago. They seem to really enjoy mixing his parts up with their IM2 Tony Starch.


152 Webster, P V, 'The coarse pottery', in Davies, J L, Excavations at Trawcoed Roman Fort, Dyfed', Bull of the Board of Celtic Studies, XXXI, 1984, (259-292), 288-292.
359 Simpson, G, 'Caerleon and the Roman forts in Wales in the Second Century AD: Part I - Caerleon and Northern Wales', Arch. Cambrensis Vol 111, 1962, 103-166.
Reassesses the chronology of Caernarvon, Caerleon, Bryn y Gefeiliau, Tomen y Mur, Caer Gal, Caersws and Forden Gaer on coin &: pottery evidence. Some pottery is published here in detail for the first time.
Cretariae Romanae Fautores, Acta XXIII/XXIV, 1984, 117-122.
548 Allen, J L R & Fulford, M G, 'The Wentlooge Level: A Romano- British Saltmarsh Reclamation in Southeast Wales', Britannia XVII, 1986, (91-1 17), 102-105.
549 Boon, G C, Laterarium Iscanum: The Antefixes, Brick and Tile Stamps of the Second Augustan Legion, National Museum of Wales, 1984, 56.
A type series of antefixes and stamps with details of find spots including those away from the legionary base.
550 Boon, G C, 'The samian ware', in Zienkiewicz, I D, The Legionary Fortress Baths at Caerleon: II. The Finds, Cardiff, 1986, 39-49. See also entry no. 551.
Dating evidence for the important Fortress Baths Groups.
Location: Legionary Museum, Caerleon 551 Greep, S J, 'The Coarse Pottery', in Zienkiewicz, I D, The Legionary Fortress Baths at Caerleon: II. The Finds, Cardiff, 1986, 50-96. See also entry no. 550.
The most important pottery report to come from Caerleon in recent decades. The overall quantity of pottery is large while the method of excavation has enabled this to be divided into a series of stratified groups. Seven lamp fragments are described by Richard Brewer (p. 96).
552Webster, P V, 'The pottery', in Burnham, B C & M B, 'Recent survey work on the fort and vicus at Pumpsaint', Carmarthenshire Antiquary XXII, 1986, (3-13), 7-12.
A small collection which includes an anomalous pit group with late 1st century samian and coarse pottery of the mid 2nd century. Further excavation may explain the divergence or perhaps all are the result of tidying up on demolition of the fort in c160. This is the only pottery so far published from the Pumpsaint (Dolaucothi) fort.
802 Allen, JR L & Fulford, M G, 'Romano-British Settlement and Industry on the Wetlands of the Severn Estuary', Antiq J, VoL 67, 1987, 237-289.
Finds from coastal fieldwork which give a useful cross-section of local ceramics.
803 Evans, D R & Metcalf, V M, 'Excavations at 10 Old Market Street, Usk', Britannia, Vol. 20, 1989, 23-68.
Most of the pottery from this excavation was lost in a fire at the Glamorgan-Gwent Archaeological Trust Headquarters. That, published is not, therefore, a representative sample but a result of a (considerable) salvage operation. Thus we have a complete samian report but no illustrations, a small amount of coarse pottery and amphorae and a more complete sample of the mortaria.
804 Greep, 5, 'Romano-British Coarse Pottery', in Britnell, W, 'The Collfryn Hillslope Enclosure, Llansantffraid Deuddwr, Powys; Excavations 1980-1982', Proc Prehist Soc, Vol 55, 1989, (89- 134), 126 & microfiche 2.6.
Plain ware only from a ceramically poor site.


This fresh and engaging book looks at each of the Roman emperors from Julius Caesar in 44BC to Romulus Augustulus in AD 476, illuminating not only the manner of their deaths but what their final days tell us about their lives. We also hear how the most powerful position in the history of the Western world held a permanent appeal, despite its perils, with eager candidates constantly coming forward to seize the throne.
Very few of the Roman emperors died a natural death. The insane Caligula was murdered after leaving the theatre; Caracalla while he was relieving himself. Caesar was stabbed twenty three times and Otho was dragged into the Tiber with a flesh-hook. However great an emperor's power, danger was ever present.
Emperors Don't Die in Bed provides a clear history of the imperial succession as well as a compelling depiction of the intrigue and drama of Roman imperial politics.


text:
Open letter to the World Health Organization (WHO) and its Member States
We are writing to ask the WHO and its Member States to support the proposal by Costa Rica for the creation of a global pooling mechanism for rights in the data, knowledge and technologies useful in the prevention, detection and treatment of the coronavirus/COVID-19 pandemic.
(Copy of letter from Carlos Alvarado Quesada, Presidente de la República, Costa Rica, and Daniel Salas Peraza, Ministro de Salud, Costa Rica, to Dr. Tedros Adhanom Ghebreyesus, Director-General of the World Health Organization, available here).
Costa Rica correctly saw this as a pool with a diverse set of rights, including those relating to patents on inventions and designs, regulatory test data, research data including outcomes, know-how, cell lines, copyrights and blueprints for manufacturing, as these rights relate to equipment, diagnostic tests, devices, medicines, vaccines, and other medical tools.
Such a pool would allow for competitive and accelerated production of needed COVID-19 technologies, and expand our capacity to address the need for affordable products for all.
The inputs to such a pool could come from governments that fund research and development or buy innovative products, as well as from universities, research institutes, charities, private companies and individuals who control rights.
The WHO should immediately reach out to Member States that are funding biomedical research relevant to the current pandemic, and engage other rights holders as well.
We recognize that some governments and other entities may be reluctant to openly share technologies globally, such as by open licensing or licensing on reasonable and affordable royalties, when there is uncertainty about whether others will make similar commitments.
To move forward as quickly as possible, and consistent with the Costa Rica proposal, the WHO can put forth an initial phase-one agreement that creates the bare minimum legal basis to permit such assignments/licenses in the future, such as by including options in funding contracts, and create a process for working out the details at a later date, including the ultimate decisions on which technologies to share, and the terms of the authorizations, including possible remuneration. As rights holders work with the WHO and deepen their understanding of the challenges we face in responding to the pandemic, the logic and benefits of cooperation and global pooling will be compelling.
The most important and needed element today is leadership, to convince those funding R&D or buying innovative products that in this emergency, the broadest sharing of technology could save the most lives. Moreover, and this needs to be addressed in funding agreements, now.
Organizations (alphabetical order)
Alianza LAC-GLOBAL por el Acceso a Medicamentos
American Medical Student Association
Associação Brasileira Interdisciplinar de AIDS (ABIA)
Comité de Veeduría y Cooperación en Salud de Colombia (CVCS) / Health Oversight and Cooperation Committee (CVCS)
Creative Commons Ecuador
FUNDACION IFARMA – Colombia
Fundación Vía Libre
Global Justice Now
Grupo de Trabalho sobre Propriedade Intelectual (GTPI)
Health Action International
Health GAP (Global Access Project)
Incentives for Global Health
Just Treatment
Knowledge Ecology International
Korean Pharmacists for Democratic Society(KPDS)
Korean Federation Medical Activist Groups for Health Rights (Association of Korea Doctors for health rights, Association of Physicians for Humanism, Korean Dentist's Association for Healthy Society, Korean Pharmacists for Democratic Society, Solidarity for worker's health)
Lawyers Collective
Misión Salud
Observatorio Iberoamericano de Propiedad Intelectual (OBIPI)
People's Health Institute (Korea)
Public Eye
Red Latinoamericana por el Acceso a Medicamentos (RedLAM)
Salud por Derecho
Salud y Fármacos EEUU
SELACC (the secretariat of Cáritas Latin America and the Caribbean)
STOPAIDS
T1International
UAEM Europe
Union for Affordable Cancer Treatment (UACT)
Universities Allied for Essential Medicines (UAEM)
Global Health Law Committee, International Law Association
Frederick Abbott, Co-Chair, Edward Ball Eminent Scholar Professor, Florida State University College of Law, USA
Brigit Toebes, Co-Chair, Professor and Chair, Health Law in a Global Context, Faculty of Law,University of Groningen, The Netherlands
Ellen ' t Hoen, Co-Rapporteur, Director Medicines Law & Policy and University Medical Centre Groningen.
Including the following Members:
Ryan Abbott, Professor of Law and Health Sciences, University of Surrey, United Kingdom and Adjunct Asst. Prof. of Medicine, David Geffen School of Medicine at UCLA, USA
Pia Acconci, Full professor of international law, Faculty of Communication Science, University of Teramo, Italy
Wang Chenguang, Professor of Law, Tsinghua University, China.
Andre den Exter, Universitair hoofddocent Gezondheidsrecht (University professor Health Law), Jean Monnet Chair EU Health Law, Erasmus School of Law, The Netherlands
Hélène De Pooter, Maître de conférences en droit public à l'Université Bourgogne Franche-Comté – CRJFC, France
Gian Luca Burci, Adjunct Professor of International Law, Graduate Institute of International and Development Studies, Geneva, Switzerland
Mihalis Kritikos, Scientific Foresight Unit (STOA), EPRS | European Parliamentary Research Service
Stefania Negri, Associate Professor of International Law, Department of Legal Sciences – University of Salerno, Italy
Laurent Sermet, Professeur d'Université, Institut d'études politiques, Aix-en-Provence, France
Pedro Villarreal, PhD (UNAM, Mexico), Senior Research Fellow, Max Planck Institute for Comparative Public Law and International Law, Heidelberg, Germany
Tania Voon, Professor of Law, Melbourne Law School, The University of Melbourne, Australia
Morten Walløe Tvedt Associate Professor, Molde University College, Norway, Norwegian branch.
Individuals (alphabetical order)
Barbara Handelin, PhD, CoFounder, Audacity Therapeutics
Carol A. Nacy, Ph.D., CEO, Sequella, Inc.
Charles Clift
Claudia Vaca, Profesora asociada, Directora Centro de Pensamiento: "Medicamentos, Información y Poder", Universidad Nacional de Colombia
Diane Singhroy, PhD, Virologist
Dr. Andrew Hill, Honorary Visiting Senior Research Fellow, University of Liverpool
Dr. Carina Vance, former Minister for Public Health (Ecuador), former Director of the South American Institute of Governance in Health (ISAGS) of the Union of South American Nations (UNASUR).
Dr. Guillaume Long, former Minister of Foreign Affairs (Ecuador)
Dr. Hernán Núñez Rocha, former Director of the Ecuadorian patent office
Dr. Jennifer Sellin, Assistant Professor Dept. of International & European Law, Faculty of Law, Maastricht University, Maastricht Centre for Human Rights
Dr. René Ramírez Gallegos, former Minister of Higher Education, Science, Technology and Innovation in Ecuador
Dr Ruth Lopert MD MMedSc FAFPHM, Director, LWC Health
Ellen 't Hoen LLM PhD, Director, Medicines Law & Policy
Fifa Rahman, PhD Candidate, Intellectual Property and International Trade, University of Leeds
Gregg Alton, Former Chief Patient Officer Gilead Sciences, Inc.
Hannes Braberg, PhD, Staff Scientist at University of California, San Francisco
Jennifer Cohn, MD MPH, Assistant Professor, Division of Infectious Diseases, University of Pennsylvania School of Medicine
Jennifer Milena Bueno, SLP MsC, Coordinadora CVCS, Investigadora en comunicación-educación en salud
Jordan Jarvis, MSc, DrPH Candidate, London School of Hygiene & Tropical Medicine, UK; Visiting Researcher, MAP-Centre for Urban Health Solutions, St. Michael's Hospital, Toronto, Canada
Jorge Bermudez, MD, DSc; Public Health Researcher at Fiocruz, former Executive-Director of UNITAID, former Member of the UN Secretary-General High-Level Panel on access to Medicines
Katrina Perehudoff MSc LLM PhD, Post Doctoral Research Fellow, Dalla Lana School of Public Health, University of Toronto, Canada, Post Doctoral Assistant ('doctor assistent'), Department of Public Health & Primary Care, Ghent University, Belgium
Lilianne Ploumen, Member of Parliament, PvdA Spokesperson for Foreign Affairs, Curative care and She Decides
Luc Denys, Belgium, jurist, retired J & J
Luis Villarroel Director, Corporacion Innovarte, Ex Miembro Tribunal Propiedad Industrial de Chile
Luz Marina Umbasia Bernal, GHP Corp.
Manuel Becerra Ramírez, Universidad Nacional Autónoma de México
Marcel Canoy, economist, Erasmus School of Accounting and Assurance
Oscar Lizarazo-Cortés, Universidad Nacional de Colombia-Sede Bogotá
Paul Fehlner, President & CEO, reVision Therapeutics, Inc.
Peter B. Bach, MD, MAPP, Director, Center for Health Policy and Outcomes, Memorial Sloan Kettering Cancer Center
Prof. Brook K. Baker, Northeastern U. School of Law, Program on Human Rights and the Global Economy, and Senior Policy Analyst, Health GAP
Prof. Dr. H.D. Banta, former director of the Health Program US Congressional Office of Technology Assessment and former Deputy Director of the Pan American Health Organization
Professor Paulo D. Picon MD, PhD, Full Professor of Internal Medicine, Universidade Federal do Rio Grande do Sul, Brazil
Rafael Pérez Miranda, Universidad Autónoma Metropolitana
Sol Terlizzi, Academic Coordinator, Master in Intellectual Property, FLACSO Argentina
Suerie Moon, MPA, PhD, Co-Director, Global Health Centre, Graduate Institute of International and Development Studies, Geneva
Tony Quinones, Bright Path Laboratories, Inc.
Yannis Natsis, Management Board member, European Medicines Agency.
More information in this article by Brook Baker.
Duque Fernán Núñez, 2.
saludporderecho@saludporderecho.org


to view the complete version of this paper.
Abstract: Particle oxidation catalysts (POC) are specialized diesel oxidation catalysts that utilize substrates with some capacity to capture solid particulates. The captured soot is then oxidized through reactions with nitrogen dioxide. POCs are passive devices, with PM emission reduction efficiency higher than that of the DOC, but lower than diesel particulate filters. Particle oxidation catalysts are a relatively new emission control technology—some aspects of their performance remain not fully characterized.
Definition. Particle oxidation catalysts (POC) are devices that can capture and store carbonaceous PM material for a period of time sufficient for its catalytic oxidation, while having open flow-through passages that allow exhaust gases to flow, even if the PM holding capacity is saturated. In other words, the particle oxidation catalyst is a specialized diesel oxidation catalyst with a capacity to hold solid soot particles. The captured particles must be removed from the device through oxidation to gaseous products, in a process called regeneration. The POC regeneration is typically accomplished via reactions between soot and nitrogen dioxide, generated in an upstream NO2 catalyst. Contrary to the diesel particulate filter (DPF), the POC will not plug once filled with soot to its maximum capacity in the absence of regeneration. Rather, the PM conversion efficiency will gradually decrease, allowing the PM emissions to pass through the structure.
Biophotovoltaic is an adjective used to define a device in which a fraction of the electrons produced during the oxidation of water by photosynthesis are transferred onto an anode and then to a cathode where an electrically driven process takes place.


In Ellen's Tale, Alberta Ross gives us an historical romance set in the future. She alternates between two main love stories occurring in different time periods.
Ellen's Tale makes for almost scary reading as the descriptions of climate change, child soldiers, landmines and genetic engineering that lead to mass death, disasters and despair, ring all to true to current events seen in the news.
Alberta Ross creates her own vision of how the world will become and the steps that will be needed to be taken to save humanity over the years showing a real ease in world building and scene setting. This is one book that will leave you thinking about where our world is heading.
The main love story is between Ellen, a girl from the cities and Bix, a rider who was genetically modified as a child to fight. Their story has many twists and turns and the road to their happily ever after effects all mankind.
The other love story that grows through out the book is that between Maia, a young researcher and Ris, an expert on Ellen (who lived 50 years previously).
A thought provoking and entertaining read that will have you cheering for the characters right from the beginning. In my opinion, a book well worth reading.


text:
Lawmakers Speak Out Against Bill Aimed at Ballot Initiatives
(KLIX) – As a bill that seeks to make it more difficult for volunteer-driven initiatives to get off the ground moves closer to the Senate floor, Idaho democrats are speaking out.
The Senate Affairs Committee in a hearing on Wednesday voted 6-3 to send Senate Bill 1159 to the Amending Order.
"Most of the amendments are cosmetic updates, and they will not fix this bill's rotten foundation," Rep. Mat Erpelding said in a statement on Wednesday, noting that in his opinion the intent of the bill is to retaliate and suppress voters. "You can't put lipstick on a pig."
Some lawmakers say the legislation is an attempt to limit Medicaid expansion in Idaho, which voters approved 61 percent last November. The ballot initiative would provide access to some 91,000 low-income residents, according to a report by the Associated Press, with the federal government picking up about 90 percent of the estimated $400 million cost.
Republican Sen. Scott Grow of Eagle, sponsor of SB1159, said his measure is not intended to attack the Medicaid expansion ballot initiative, and that it wouldn't be affected anyway because it already passed.
Democrats say otherwise, calling the Senate bill the "Revenge on Voters Act."
Eperlding and two other Democrat senators issued a joint statement on Wednesday, saying that hours of opposing testimony and thousands of emails did not appeal to the majority's conscious and that the only testimony in favor of the bill came from lobbyists.
Michelle Stennett, a senator from Sun Valley, said she fears the bill would allow companies and big money will take over the process and peddle initiatives from a national platform.
Stennett said that it was unfair for the legislature to hold ballot initiative volunteer groups to a higher standard than the legislature itself. Notably, requiring volunteers to provide a fiscal note and know the costs of a ballot initiative before beginning the process.
"They will bring initiatives that are not an upwelling from our own politics, our own people," she said. "Amendment or not, this bill will have the same dangerous, undemocratic outcome."
Also on Wednesday, House Bill 277 sponsored by Rep. John Vander Woude, a Medicaid expansion restrictions bill, was voted out of the House Health and Welfare Committee, 10-3.
Burley Sen. Fred Martin introduced a compromise bill in Senate State Affairs, which includes minimal restrictions and access to a voluntary work-training program.
SB1159 will now undergo edits before hitting the Senate floor.
Categories: Featured, Idaho News


text:
Калифорнски () — статистически обособленная местность, расположенная в боро Кенай (штат Аляска, США) с населением в 7850 человек по статистическим данным переписи 2010 года.

География
По данным Бюро переписи населения США статистически обособленная местность Калифорнски имеет общую площадь в 181,56 квадратных километров, из которых 179,23 кв. километров занимает земля и 2,59 кв. километров — вода. Площадь водных ресурсов составляет 1,43 % от всей его площади.

Статистически обособленная местность Калифорнски расположена на высоте 16 метров над уровнем моря.

Демография
По данным переписи населения 2000 года в Калифорнски проживало 5846 человек, 1596 семей, насчитывалось 2117 домашних хозяйств и 2479 жилых домов. Средняя плотность населения составляла около 32,6 человек на один квадратный километр. Расовый состав Калифорнски по данным переписи распределился следующим образом: 89,75 % белых, 0,24 % — чёрных или афроамериканцев, 4,6 % — коренных американцев, 0,67 % — азиатов, 0,09 % — выходцев с тихоокеанских островов, 4,05 % — представителей смешанных рас, 0,6 % — других народностей. Испаноговорящие составили 1,97 % от всех жителей статистически обособленной местности.

Из 2117 домашних хозяйств в 42 % — воспитывали детей в возрасте до 18 лет, 62,3 % представляли собой совместно проживающие супружеские пары, в 8 % семей женщины проживали без мужей, 24,6 % не имели семей. 19,4 % от общего числа семей на момент переписи жили самостоятельно, при этом 2,5 % составили одинокие пожилые люди в возрасте 65 лет и старше. Средний размер домашнего хозяйства составил 2,74 человек, а средний размер семьи — 3,13 человек.

Население статистически обособленной местности по возрастному диапазону по данным переписи 2000 года распределилось следующим образом: 31,3 % — жители младше 18 лет, 6,1 % — между 18 и 24 годами, 31,5 % — от 25 до 44 лет, 25,6 % — от 45 до 64 лет и 5,4 % — в возрасте 65 лет и старше. Средний возраст жителей составил 35 лет. На каждые 100 женщин в Калифорнски приходилось 107,5 мужчин, при этом на каждые сто женщин 18 лет и старше приходилось 107,1 мужчин также старше 18 лет.

Средний доход на одно домашнее хозяйство в статистически обособленной местности составил 54 864 доллара США, а средний доход на одну семью — 58 750 долларов. При этом мужчины имели средний доход в 50 583 доллара США в год против 30 493 доллара среднегодового дохода у женщин. Доход на душу населения в статистически обособленной местности составил 23 898 долларов в год. 6,6 % от всего числа семей и 7,9 % от всей численности населения находилось на момент переписи населения за чертой бедности, при этом 9,2 % из них были моложе 18 лет и ни одного в возрасте 65 лет и старше.

Примечания

Статистически обособленные местности Аляски
Кенай

redpajama_set_name: RedPajamaWikipedia


text:
bool OpPlusParser::judge(const std::string& token) { return token == "+"; }
OpPlusParser::InfoType OpPlusParser::get(const std::string& token) { return 0; }

bool OpMinusParser::judge(const std::string& token) { return token == "-"; }
OpMinusParser::InfoType OpMinusParser::get(const std::string& token) { return 0; }

bool OpMultiplyParser::judge(const std::string& token) { return token == "*"; }
OpMultiplyParser::InfoType OpMultiplyParser::get(const std::string& token) { return 0; }

bool OpDivideParser::judge(const std::string& token) { return token == "/"; }
OpDivideParser::InfoType OpDivideParser::get(const std::string& token) { return 0; }

bool OpDefineParser::judge(const std::string& token) { return token == "define"; }
OpDefineParser::InfoType OpDefineParser::get(const std::string& token) { return 0; }

bool OpMacroParser::judge(const std::string& token) { return token == "macro"; }
OpMacroParser::InfoType OpMacroParser::get(const std::string& token) { return 0; }

bool OpLambdaParser::judge(const std::string& token) { return token == "lambda"; }
OpLambdaParser::InfoType OpLambdaParser::get(const std::string& token) { return 0; }

bool OpIfParser::judge(const std::string& token) { return token == "if"; }
OpIfParser::InfoType OpIfParser::get(const std::string& token) { return 0; }

const TokenType OpPlusParser::type = OpPlus;
const TokenType OpMinusParser::type = OpMinus;
const TokenType OpMultiplyParser::type = OpMultiply;
const TokenType OpDivideParser::type = OpDivide;
const TokenType OpDefineParser::type = OpDefine;
const TokenType OpMacroParser::type = OpMacro;
const TokenType OpLambdaParser::type = OpLambda;
const TokenType OpIfParser::type = OpIf;


text:
package com.linkedin.parseq.promise;

/**
 * A {@link Promise} that can have its value set.
 *
 * @author Chris Pettitt (cpettitt@linkedin.com)
 */
public interface SettablePromise<P> extends Promise<P>, Settable<P> {
}


text:
var test        = require('tap').test,
    response    = require('../../lib/response');

test('response', function (t) {
    // Setup
    response.headersSent = false;

    response.writeHead = function (code, headers) {
        t.equal(code, 404, 'code is of expected value');
        t.type(headers, 'object', 'headers is of expected type');
        t.equal(headers['Content-Type'], 'text/html', 'expected content type');
        t.equal(headers['Content-Length'], 13, 'expected content length');
    };

    response.end = function (body) {
        t.type(body, 'string', 'body is of expected type');
        t.equal(body, '', 'body is of expected value');
        t.end();
    };

    // Exec
    response.html(404, '');
});


I'm a university student striving to earn a bachelors degree in English literature. Storytelling is one of my main passions, but I'm also very interested in a multitude of things such as music, art and acting.
My interest in online voice acting sparked in 2013. From then, I had the opportunity to take a theatre introduction course at my university, and an improvisation class at Comedy Sportz.
I'm hoping to gain voice-over experience by participating in projects, so I look forward to potentially getting the chance to work with you!
I don't mind working for free as long as I'm credited in the project. I'm currently hoping to gain experience.


text:
Q: Файл лога не уменьшается в размере Жила-была небольшая база, размером 15Гиг на MSSQL 2012
метода восстановления Простой
в какой-то момент файл с журналом вырос до максимального размера указанного в настройках и резервные копии каждый день начали прибавлять по 2 гига
процедура сжатия файлов не запускается.
как почистить файл с логом и сделать размер резервной копии вменяемого размера, сейчас она уже 70 Гигов


I'm Rosario and I live with my husband and our two children in Baarle-Nassau, in the NB south part. My hobbies are Worldbuilding, Paintball and Lapidary.
When you have any kind of concerns relating to where by in addition to how you can make use of 挂机游戏破解, you can email us from the internet site.


Today is my 14th day of not smoking. I'm feeling pretty good about that. There was a lot of fear of failure behind this quit. I'm not out of the clear by any means. Just feeling good about the journey so far.
Last week I felt pretty emotionally out of wack. A little crying, lots of irritations mostly little nothings. This week I'm starting out tired and very mentally foggy. Yes I am getting good sleep with the help of an herbal sleep aid. And I ate well all day. I do think it's just my system readjusting after nicotine being withdrawn. I stopped my patch Friday night so it has been close to 72 hours.And I'm nicotine free as well as not smoking.
I had a good two week journey using the nicotine patch which I'll review in more detail in another blog.
Tonight my daughter lit up right in front of me while we were sitting outside. I felt a small twinge of wanting to smoke. Then it was gone. I didn't even struggle too much.
I still spend almost every moment thinking about not smoking or analyzing how I'm feeling based on what I've learned about nicotine withdrawal. But the urges and craves aren't as strong. at least for now. I've changed up my morning routine so I'm in bed later doing stretches then just head to the shower. That has really helped the morning craves. I barely think about smoking in the a.m. The car is now a no brainer. The thought doesn't even come up. I get a little crave after breakfast but I use an herbal lozenge and it goes away. In fact I hardly had a crave today. The weekends I still have to keep pretty busy. I find I want to take a break and smoke. But...."I don't do that anymore. What can I do instead?" Deep breathing is one of my main go to's as well as sitting in our greenhouse and communing with the plants. And I can't tell you what a lifesaver cinnamon sticks have been. Especially on the weekend when I'm around my smoking partner a lot more. If I get a crave I can just chomp the dickens out of it and it can take the abuse plus give me a little hint of that cinnamon flavor after I work it awhile. I even keep one at work.
And water. Lots and lots of water, especially at work. Lemon water worked well for the weekend. I have used lots of herbal no smoking lozenges. I'm not really sure they do anything, but by the time I'm done sucking on them the crave is gone so the purpose is served either way.
I still wake up with a middle of the night crave, though it is not as strong as that first one I sent out a help call for. Still breathing through it and using a Bach Rescue Remedy. I am concerned about this being a vulnerable spot for me. I am a regular waker in the wee hours always have been. Smoking was a big part of I'll just sit here in the quiet and smoke then go try and sleep. A suggestion of crossword puzzles was made, but if I stimulate too much then I can't go back to sleep.I downloaded a meditation app that I want to try here if I can remember. It is the middle of the night when I'm trying to think.
Thanks to all of you Exers who have supported me through these first few days. Your support and guidance has been immeasurable.. And darn it elvan I finally got those bubbles on my list, but the list didnt get to the store., Figures, huh?
I use Bach's Rescue for my kitties sometimes, I completely forgot people can take it too! that's a good idea. I'm not sure which app you're using but I know Insight Timer has guided meditations as well as background music to fall asleep to. Rain and thunder usually put me out pretty quick.
Whoo, you are so strong to be able to handle your daughter smoking right in front of you - keep that up and these two weeks will soon be fading away in that rearview mirror. Nicely done!
Fantastic blog. You said so much about the ups and downs, hope and worry, trials and successes that make up early smobriety. So likely somebody new came along today and read that you are making it work one day at a time. Congratulations. (When you described your daughter's lighting up, yeah, I can imagine that too, and yeah a flicker of something for me too, but it's gone...just like that!). Thanks for sharing.
GREAT blog...sorry about the bubbles...I forgot them so many times and I cannot count the number of times I have forgotten my list. I have gone to the store planning to make spaghetti and meatballs and gotten home and started the sauce and the meatballs and then realized that I didn't get the pasta. GRRRRRR!
You are doing GREAT. I used to awaken during the night and sometimes get up and go outside and smoke. It was weird because I never smoked indoors and the place I smoked was downstairs and outside on the deck. I am not sure when it stopped but it did and I NEVER think of smoking during the night any more.
Congratulations on a SOLID quit!
Congratulations on passing the 2 week mark.
You're doing great. Remember to celebrate EVERY day of freedom! We're celebrating right along with you.
So proud of you! For the fourteen days and for getting through the cravings and temptations. Every day gets a little better!


While meeting in a high school auditorium, Heartland World Ministries Church purchased a 37,558 sq. ft. two-story office building intending to renovate it into a permanent home for the Heartland School of Ministry. DLA was commissioned to renovate the building and in the process determined a great deal more space was available than the school required.


Obituaries for the last 7 days on Your Life Moments. To help us for a better experience we recommend disabling your ad blocker. Driver frequency list nascar 2014.
NASCAR on ESPN was the coverage of NASCAR on ESPN, ESPN2, and ABC. ABC, and later ESPN, carried NASCAR races from the sanctioning body' s top three divisions at. Numerous conspiracy theories pertain to air travel and aircraft.
Incidents such as the 1955 bombing of the Kashmir Princess, the 1985 Arrow Air Flight 1285 crash, the 1986 Mozambican Tupolev Tu- 134 crash, the 1987 Helderberg Disaster, the 1988 bombing of Pan Am Flight 103 and the 1994 Mull of Kintyre helicopter crash as well as various aircraft technologies and alleged sightings. Postmedia Solutions gives you the power to grow your business.
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While Tiny Boxwoods is a totally logical choice for the top spot, the author's failture [sic] to include both Pondicheri's chocolate oatmeal chili cookies and Barnaby's chocolate chip cookies is an absolute shonda [sic].
Apparently he was so enraged he forgot to hit spell-check. 'Cause I think he meant schande, though a tiny part of me hopes he actually thinks I'm cool enough to be compared to this woman. Anyway, I knew Eric et al. were on to something, so I decided to make a trip to Baby Barnaby's to taste the excluded cookie.
I've long been a fan of Baby Barnaby's (I especially relish their pumpkin pancakes), so it would be no surprise to me if they served a decent chocolate cookie.
According to their menu, they actually offer "the best chocolate chip cookie" for a mere two dollars. I picked up one to go and ate it a few hours later with some hot cocoa in front of a roaring heater.
Slightly crunchy. Crumbling, buttery interior. Very dense with thin semisweet chocolate chunks.
Yes, good enough to be on the list. Mea culpa. Thanks, readers, for alerting me to my wrongful omission.
Just don't ask me which other chocolate chip cookie on the countdown I'd swap out for Barnaby's.