And so I arrived at my hotel, checked in to my room and then proceeded to tweet my problem to anyone on Twitter who cared to read it. This is known as sentiment tracking, a method that may well come in useful in education in the future. How does sentiment tracking work?
Not a problem, said KLM. Actually, that is a problem for me, I pointed out. Known as ' sentiment tracking ', or 'opinion mining', many of the larger businesses now monitor social media channels for mentions of their company name.
As I have continued to dig deeper into why ROI is not common in the learning space, it is clear the people who serve the learners are not the problem… so then what is it? I have concluded that there are 3 parts to this problem – and the good news is that all of them are solvable. Problem 1: The Shortage of Code Wizards. Problem 2: Third Party Data. Track Data Easily. Problem 3: The CFO. The real data to track ROI is worth the change.
Collaborative/cooperative online learning events, especially when built on problem-based learning (PBL) design approaches and facilitated by a guide-on-the side ( eWorkshops ) are more likely to adhere to the principles. The problems are typically solved differently by every team.
Channels members have their own difficulties as well, often struggling with onboarding issues, portal access, certifications and a host of other problems holding the partner back. The post Partner Problems – 5 Common Challenges Channel Networks Face appeared first on Docebo.
The problem is that the novelty is actually distracting. The first time one of my colleagues tried on a VR headset, the goal in question was to drive a virtual sports car around a track. The post 7 practical problems with VR for eLearning appeared first on LearnUpon.
The learning department was simultaneously updating the company's outdated learning management system with a more robust solution that could customize content for specific employees, allow managers to track their team's progress, and integrate with Guild's broader human resource management system.
Tweet In the second of a series of blog posts on helping L&D move forward, I look at how we need to help workers gain immediate access to "learning&# that solves their performance problems.
design a curriculum solution that: • has a clear goal tied to a well- articulated business problem, • meets the needs of your target. to solve the business problems that need solving. clear on your business problem and desired outcomes. problem? problem and desired result.
What if the social learning platform can track, measure, and even predict a learner's behavior? Challenges faced included the following: To encourage a peer-to-peer problem-solving approach between employees.
We can connect people socially, upload user generated content, and track and. Living up to the Promise of eLearning: CLOSING THE LEARNING-DOING GAP A FAILED PROMISE 2 kineo.com info@mplus.kineo.com 312-846-6656 OUTCOMES VS CONTENT Part of the problem might be that we've.
If you feel the need to explain your problem more in detail you can always sign up for one of our QnA sessions we have three times a week! The post Keep track of Easygenerator's updates appeared first on Easygenerator The Easygenerator development team releases new fixes and features every week. Check out our new product update page to stay informed on all new updates.
Navigating the digital ecosystem, preselling, and the problems with the culture of free with Robin Harris in this episode of the LMScast podcast with Chris Badgett of LifterLMS. We talk a lot on this show and I go on and on about it, the five hats problems.
After the advent of Learning Management Systems, managing learners may seem a problem with an obvious answer. Mobile Learning Mobility Offline Learner Management Offline Mobility Tracking Offline Learning PathSo why has it reared its head again? Well, it has and it hasn't. The typical context in which learners access training from within the cyber and physical boundaries of the organisation, poses no challenge any more. However, […].
JobAdder provides an ATS that enables more than 8,000 recruiters match candidates to jobs, track the candidates' progress, manage job orders, and more. The post How Do Top Applicant Tracking Software (ATS) Providers Boost User Adoption Rates?
the problem? the content, we then tend to lose track of participants. her own performance problem. FOUR WAYS TO CLOSE THE. LEARNING-DOING GAP FOR. FRONT-LINE MANAGERS 4FOREWORD We're in business to help organizations. achieve their goals by making sure their.
Do you track and certify people over time? Competition for talent requires a long-term view of capabilities development. Capability development is a never-ending challenge. Every organization has a combination of new hire, technical, systems and technology training, project management and professional development, and leadership development challenges. Worse, companies are always moving into new business areas that demand new skills.
It is the reason you can get your e-learning course from one vendor and still launch and track it from the to be integrated with one another – to "talk" to each other. And, sometimes the reason is because there is a problem with the SCORM set up. When your SCORM package isn't tracking right, your vendors can help you test the SCORM to see if there is a problem. What if SCORM isn't the problem?
After 10+ years of salvaging presentations (and professional reputations) I thought it was time to compile some answers for three of the most universally puzzling PowerPoint problems: 1. How do I add a background audio track to my PowerPoint?
They dont involve real-world problem-solving or decision-making. As flexible social learning environments, MOOCs provide opportunities for collaboration, project-based learning, and real-world problem-solving. The first problem is that this is boring.
I ran into a problem this week involving Moodle and SCORM and wanted to share the problem and solution for my own good and for the good of anyone else out there who may be having a similar problem.
One "problem" with elearning as it is reported to me is that learners just take the assessment without doing the learning. So I would argue that the only thing that need be tracked is the assessment and let everything else go - effort would be better spent in designing learning resources that are useful and appropriate as job aids, reference works, neat little broadcasts to keep people up to date and support informal learning rather than hamstrung mandated learning that no-one enjoys.


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Amanda Dortch, an undergraduate at Tougaloo College in Jackson, MS joined the lab for the summer.
Amanda is studying the role of gender and circadian phase on object recognition memory.
Krishan Aghi received his bachelor of science degree in Neuroscience and completed his honors work in the Burwell lab.
He used a disconnection paradigm to study how the perirhinal and postrhinal cortices interact in contextual learning. In the fall, Krishan will begin study in the Berkeley Neuroscience Graduate Program.
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Dr. Heimer-McGinn studies the brain's ability to interpret environmental context, which informs the cognitive processes that guide behavior. Her NRSA proposal, titled ""Perirhinal contributions to postrhinal representations of context", is guided by the hypothesis that the rat postrhinal cortex (POR) combines spatial information with object information received from the perirhinal cortex (PER) in order to form complex representations of context. Dr. Heimer-McGinn will employ experimental lesion, electrophysiology, and optogenetic approaches in behaving rats to test this hypothesis.
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Rebecca Burwell delivered the Keynote address at the annual Women in Learning luncheon at the Annual Convention of the American Psychological Association
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Krishan Aghi wins the Royce Fellowship to begin his honors work in the summer of 2014
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Inês Tomás Pereira is awarded a fellowship from Brown University's Center for Vision Research.
Dr. Pereira is spending her fellowship working studying the role of the perirhinal and postrhinal cortices on visual object recognition using a spontaneous object recognition task in combination with electrophysiology and optogenetics.
Ho and Heimer-McGinn give presentation at Wheeler School
Jonathan Ho and Victoria Heimer-McGinn gave a presentation in the Scientific Lecture Series at Wheeler School in Providence, RI. Jonathan and Victoria outlined their colorful career paths and gave the students a flavor of their research carried out in past and present laboratories. The students, ranging from high school freshmen to seniors, showed great interest in the lectures and were very welcoming to their guests. Shown are Jon on the left and Victoria on the right with Layla Kazemi, Sara Kazemi, and Kathleen Sai-Halasz.
Lisa Dokovna receives her Masters of Science in Psychology
Lisa completed her thesis entitled, "The Neural Basis of Attention: Interconnections of the Lateral Posterior Nucleus and Postrhinal Cortex of the Rat." Congratulations!
Kristin Marie Kerr Scaplen receives her PhD in Neuroscience
Kristin's thesis is entitled, "Landmark and object processing in the rodent hippocampal system: Implications for spatial memory." Her committee members were Julie Kauer, James Knierim, and David Sheinberg. Congratulations!
Jonathan Ho and Tara Jacobson win a grant from Plexon to publish in JoVE
Jon and Tara submitted the winning abstract titled "Getting the most out of your rats: fully automated cognitive tasks for recording neural activity using a floor projection maze." Congratulations!
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The Llama Park is pleased to announce the first marriage and wedding to take place at the Llama Park in its newly decorated Marriage Barn on Saturday 26th July.
This marriage has attracted a great deal of press coverage and interest from both the Press and Media as well as from prospective Brides and Grooms looking for somewhere different to 'tie the knot'. Other weddings have already been booked for the summer and this is an exciting development for the Park.
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To find out more about the Ashdown Forest Llama Park, visit their website or contact the Management for further information on 01825 712 040.


text:
\section{Introduction.}\label{intro}

\section{Introduction}
A common practice in the management of global supply chains is \emph{dual-sourcing} (cf. \citet{Rao00}).  Under a dual-sourcing strategy, the companies usually purchase their materials from a regular supplier at a lower cost, but they are also able to obtain materials from an expedited supplier at a higher cost under emergency circumstances. For example, in the summer of 2003, Amazon used FedEx to deliver the new Harry Potter more promptly and maintained regular shipping via UPS (cf. \citet{Kelleher03}, \citet{Veeraraghavan08}). \citet{Allon10} describes an example of a $\$10$ billion high-tech U.S. company that has two suppliers, one in Mexico and one in China. The one in Mexico has shorter lead time but higher per-unit ordering cost; the one in China has longer lead time (5 to 10 times longer) but lower per-unit ordering cost. The company takes advantage of the dual-sourcing strategy to meet the demand more responsively (from Mexico) as well as less expensively (from China).

Although dual-sourcing is attractive, and very relevant to practice, optimizing a dual-sourcing inventory system is notoriously challenging.  Such inventory systems have been studied now for over forty years, but the structure of the optimal policy remains poorly understood, with the exception of when the system is consecutive, i.e., the lead time difference between the two sources is exactly one.  More specifically, the earliest studies of periodic review dual-sourcing inventory models include \citet{Barankin61}, \citet{Daniel63}, and \citet{Neuts64}, which showed that base-stock (also known as order-up-to) policies are optimal when the lead times of the two sources are zero and one respectively. \citet{Fukuda64} extended the result to general lead time settings as long as the lead time difference remains one. \citet{Whittmore77} showed that the optimal policy is no longer a simple base-stock policy when the lead time difference is beyond one and the structure of the optimal policy can be quite complex. Furthermore, it is well known that a dual-sourcing inventory system can be regarded as a generalization of a lost-sales inventory system (cf. \citet{Sheopuri10}).  Indeed, the intractability of both the dual-sourcing and lost-sales inventory models has a common source - as the lead time grows, the state-space of the natural dynamic programming (DP) formulation grows exponentially, rendering such techniques impractical.  This issue is typically referred to as the ``curse of dimensionality" (cf. \citet{Karlin58}, \citet{Morton69}, \citet{Zipkin08b}), and we refer the reader to \citet{Goldberg12} and \citet{Xin14a} for a relevant discussion in the context of lost-sales inventory models.

There is a vast literature investigating periodic review dual-sourcing inventory models as well as their variants, and we refer the interested reader to the survey of \citet{Minner03}, as well as e.g. the more recent works of \citet{Feng06}, \citet{Fox06}, \citet{Chen13}, \citet{Huggins10}, \citet{Angelus15}, \citet{Boute14}, \citet{Gong14}, \citet{Song09}, and the references therein.

As an exact solution seems out of reach, the operations research and management communities have instead investigated certain structural properties of the optimal policy (cf. \citet{Hua14}), and exerted considerable effort towards constructing various heuristic policies. \citet{Veeraraghavan08} proposed the family of dual index (DI) policies, which have two base-stock levels, one for the regular source and one for the express source, and ``orders up" to bring appropriate notions of inventory position up to these levels.  \citet{Scheller-Wolf08} analyzed the closely related class of single index (SI) policies, for which the relevant notions of inventory position are different.  Both families of policies seem to perform well in numerical studies.
\citet{Sheopuri10} considered two generalized classes of policies: one with an order-up-to structure for the express source, and one with an order-up-to structure for the regular source. Their numerical experiment showed that such policies can outperform DI policies.  In the presence of production capacity costs, \citet{Boute14} studied dual-sourcing smoothing policies, under which the order quantities from both sources in each period are convex combinations of observed past demands. They analyzed such polices under normally distributed demand, and their numerical results showed that these policies performed better for higher capacity costs and longer lead time differences (between the two sources).

A simple and natural policy that is implemented in practice, which will be the subject of our own investigations, is the so-called \emph{Tailored Base-Surge} (TBS) policy. It was first proposed and analyzed in \citet{Allon10}, where we note that closely related standing order policies had been studied previously (cf. \citet{Rosenshine76,Janssen99}).  Under such a TBS policy, a constant order is placed at the regular source in each period to meet a \emph{base} level of demand, while the orders placed at the express source follow an order-up-to rule to manage demand \emph{surges}.  We refer to Mini-Case 6 in \citet{Van Mieghem08} for more about the motivation and background of TBS policies. Note that dual-sourcing inventory systems in which a constant-order policy is implemented for the regular source are essentially equivalent to single-sourcing inventory systems with constant returns, which have been investigated in the literature (cf. \citet{Fleischmann03}, \citet{DeCroix05}).

\citet{Allon10} analyzed TBS policies in a continuous review model, and their focus was to find the best TBS policy. Numerical results in \citet{Klosterhalfen11} and \citet{Rossi12} showed that TBS policies are comparable to DI policies, and outperform DI policies for some problem instances. \citet{Allon10} conjectured that this policy performs more effectively as the lead time difference between the two sources grows. \citet{Janakiraman14a} (henceforth denoted JSS) analyzed a periodic review model and studied the performance of the TBS policy. They provided an explicit bound on the performance of TBS policies compared to the optimal one when the demand had a specific structure, and provided numerical experiments suggesting that the performance of the TBS policy improves as the lead time difference grows large.

However, to date there is no theoretical justification for the good behavior of TBS policies as the lead time difference grows large, and giving a solid theoretical foundation to this observed phenomena remains a major open question.  We note that until recently, a similar state of affairs existed regarding the good performance of constant-order policies as the lead time grows large in single-source lost-sales inventory models.  However, using tools from applied probability, queueing theory, and convexity, this phenomena was recently explained in \citet{Goldberg12} and \citet{Xin14a}, in which it was proven that a simple constant-order policy is asymptotically optimal in this setting as the lead time of the single source grows large.  The intuition here is that as the lead time grows large, so much randomness is introduced into the system between when an order is placed and when that order is received, that it is essentially impossible for any algorithm to meaningfully use the state information to make significantly better decisions.  Thus a policy which ignores the state information (i.e. constant-order policy) performs nearly as well as an optimal policy.  We note that the results of \citet{Xin14a} further demonstrate that the optimality gap of the constant-order policy actually shrinks exponentially fast to zero as the lead time grows large, and provide explicit and effective bounds even for moderate-to-small lead times.

\subsection{Our contributions}
In this paper, we resolve this open question by proving that, when the lead time of the express source is held fixed, a simple TBS policy is asymptotically optimal as the lead time of the regular source grows large.  Our results provide a solid theoretical foundation for the conjectures and numerical experiments of \citet{Allon10} and JSS.   Interestingly, the simple TBS policy performs nearly optimally exactly when standard DP-based methodologies become intractable due to the aforementioned ``curse of dimensionality".  Furthermore, as the ``best" TBS policy can be computed by solving a convex program that does not depend on the lead time of the regular source (cf. JSS), our results lead directly to very efficient algorithms (with complexity independent of the lead time of the regular source) with asymptotically optimal performance guarantees.  We also explicitly bound the optimality gap of the TBS policy for any fixed lead time (of the regular source), and prove that this decays inverse-polynomially in the lead time of the regular source.  Perhaps most importantly, since many companies are already implementing such TBS policies (cf. \citet{Allon10}), our results provide strong theoretical support for the widespread use of TBS policies in practice.  Our main proof technique combines novel convexity and lower-bounding arguments,
an explicit implementation of the vanishing discount factor approach to analyzing infinite-horizon Markov decision processes (MDP), and ideas from the theory of random walks and queues.  Our methodology significantly extends the framework for analyzing inventory models with large lead times recently introduced in \citet{Goldberg12} and \citet{Xin14a} in the context of lost-sales models with positive lead times.  Indeed, in the present work we relate the performance of an optimal policy to a certain \emph{dynamic} optimization problem by applying the conditional Jensen's inequality, while in \cite{Xin14a} the relevant optimal policy could be bounded by a \emph{static} optimization problem after applying the (non-conditional) Jensen's inequality.  The inherently dynamic nature of the resulting bounds introduce several additional difficulties not encountered previously, and which we address in the present work.

\subsection{Outline of paper}
The rest of the paper is organized as follows. We formally define the dual-sourcing problem in Section \ref{ds-sec-intro}, and describe the TBS policy in Section \ref{ds-sec-TBS}.  We state our main result in Section \ref{ds-sec-main}, and prove our main result in  Section\ \ref{ds-sec-proof}.  We summarize our main contributions and propose directions for future research in Section \ref{ds-sec-conclusion}.  We also include a technical appendix in Section\ \ref{techsec}.

\section{Model description, problem statement and assumptions}\label{ds-sec-intro}
In this section, we formally define our dual-sourcing inventory problem, closely following the definitions given in \citet{Sheopuri10}.
Let $\{D_t\}_{t \in (-\infty,\infty)}, \{D'_t\}_{t \in (-\infty,\infty)}$ be mutually independent sequences of nonnegative independent and identically distributed (i.i.d.) demand realizations, distributed as the non-negative random variable (r.v.) $D$, which we assume to have finite mean, and (to rule out certain trivial degenerate cases) to have strictly positive (possibly infinite) variance.  Here we have introduced two doubly indexed sequences to prevent any possible confusion regarding dependencies of various demand realizations.  Let $\hat{G}$ be an independent geometrically distributed r.v., where $\p(\hat{G} = k) = 2^{-k}, k \geq 1$.  As a notational convenience, let us define all empty sums to equal zero, empty products to equal one, $\frac{1}{\infty} = 0$, $\mathbf{0} (\mathbf{1})$ denote the all zeros (ones) vector, and $\mathbb{I}(A)$ denote the indicator of the event $A$.  Let $L \geq 1$ be the deterministic lead time of the regular source (R), and $L_0 \geq 0$ the deterministic lead time of the express source (E), where $L > L_0 + 1$. Let $c_R,c_E$ be the unit purchase costs of the regular and express sources, and $h,b$ be the unit holding and backorder costs respectively, with $c \triangleq c_E - c_R > 0$.  In addition, let $I_t$ denote the on-hand inventory at the start of period $t$ (before any orders or demands are received), and $q_t^R (q_t^E)$ denote the order placed from R(E) at the beginning of period $t$.  Note that due to the leadtimes, the order received from R(E) in period $t$ is $q_{t - L}^R (q_{t - L_0}^E)$.  As we will be primarily interested in the corresponding long-run-average problem, and for simplicity (in later proofs), we suppose that the initial conditions are such that (s.t.) the initial inventory is $-\sum_{i=1}^{\hat{G}} D'_{-i}$, and no initial orders have been placed from either R or E.  Indeed, the associated system state will prove convenient to use as a ``regeneration point" when analyzing certain Markov chains which arise in our proofs, where we note that the geometric distribution allows us to preclude certain kinds of pathological periodic / lattice behavior which might otherwise interfere with proving the existence of relevant stationary measures.  We note that although assuming such a convenient randomized initial condition simplifies several technical proofs along these lines, such an assumption is not strictly necessary for our analysis, since the associated long-run average problem is insensitive to the particular choice of initial conditions.

As a notational convenience, we define $q_k^R = q_k^E = 0, k \leq 0$.  For $t = 1,\ldots,T$, the events in period $t$ are ordered as follows.
\begin{itemize}
\item Ordering decisions from R and E are made (i.e. $q_t^E,q_t^R$ are chosen);
\item New inventory $q_{t-L}^R + q_{t-L_0}^E$ is delivered and added to the on-hand inventory;
\item The demand $D_t$ is realized, costs for period $t$ are incurred, and the inventory is updated.
\end{itemize}
Note that the on-hand inventory is updated according to $I_{t+1}= I_{t} + q_{t-L}^R + q_{t-L_0}^E - D_t$, and may be negative since backorder is allowed.

We now formalize the family of admissible policies $\Pi$, which will determine the new orders placed.
An admissible policy $\pi$ consists of a sequence of measurable maps $\lbrace f^{\pi}_t, t \geq 1 \rbrace$, where each $f^{\pi}_t$ is a deterministic measurable function with domain $\Bbb{R}^{L + L_0 + 1}$ and range $\Bbb{R}^{+,2}$.  In that case, for a given policy $\pi$, the regular order placed in period $t$ equals $f^{\pi}_{R,t}(q_{t-L}^R,\ldots,q_{t-1}^R,q_{t-L_0}^E,\ldots,q_{t-1}^E,I_t)$; while the express order placed in period $t$ equals $f^{\pi}_{E,t}(q_{t-L}^R,\ldots,q_{t-1}^R,q_{t-L_0}^E,\ldots,q_{t-1}^E,I_t)$, and $\Pi$ denotes the family of all such admissible policies $\pi$.

Let $G(y)$ be the sum of the holding and backorder costs when the inventory level equals $y$ in the end of a time period, i.e. $G(y)\stackrel{\Delta}{=}\ hy^+  + by^-$,
where $x^+\stackrel{\Delta}{=} \max(x, 0)$, $x^-\stackrel{\Delta}{=} \max(-x, 0)$.  Here we note that $G$ is convex and Lipschitz, and for $x,y \in \bbr$,
\begin{equation}\label{Lip1}
|G(x) - G(y)| \leq \max(b,h) |x - y|\ \ \ ,\ \ \ |G(x)| \geq \min(b,h) |x|.
\end{equation}

For $t \geq L_0 + 1$, let $C_t$ be the sum of the holding and backorder costs incurred in time period $t$, plus the ordering cost incurred for orders placed in period $t - L_0$, i.e. $C_t \stackrel{\Delta}{=}\ c_R q_{t-L_0}^R +   c_E q_{t-L_0}^E + G(I_t + q_{t-L}^R + q_{t-L_0}^E - D_t).$  We note that charging in period $t$ for orders placed in period $t - L_0$ is a standard ``accounting trick" in the inventory literature to simplify various notations (cf. \citet{Zipkina}), and for the problems considered without loss of generality (w.l.o.g.).  To denote the dependence of the cost on the policy $\pi$, we use the notation $C^{\pi}_t$.  Let $C(\pi)$ denote the long-run average cost incurred by a policy $\pi$, i.e. $C(\pi) \stackrel{\Delta}{=}\  \limsup_{T\to \infty} \frac{\sum_{t = L_0 + 1}^{T} \bbe\left[C^{\pi}_t\right]}{T},$ where we again note that starting the relevant sum at $t  = L_0 + 1$ (as opposed to $t = 1$) is w.l.o.g. for the problems considered.  The value of the corresponding long-run average cost dual-sourcing inventory optimization problem is denoted by $\textrm{OPT}(L) \stackrel{\Delta}{=}\  \inf_{\pi\in \Pi} C(\pi).$

Before proceeding, it will be useful to apply certain well-known reductions to the problem at hand, where we note that similar reductions are known to hold for many classical inventory problems with backlogging (cf. \citet{Karlin58,Scarf60}).  First, as stated in cf. \citet{Sheopuri10}, for the long-run average cost problems which will be the focus of our analysis, any problem with $c_R > 0$ can be transformed into an equivalent problem with $c_R = 0$.  As such we assume throughout that $c_R = 0$.  Let us define the so-called \emph{expedited inventory position} at time $t \geq 1$ as $\hat{I}_t \stackrel{\Delta}{=} I_t + \sum_{k = t - L_0}^{t-1} q_k^E + \sum_{k = t - L}^{t - L + L_0} q_k^R$, which corresponds to the net inventory at the start of period $t$ plus all orders to be received in periods $t,\ldots,t + L_0$ (which were placed before period $t$), and the \emph{truncated regular pipeline} at time $t$ as the $(L - L_0 - 1)$-dimensional vector $\mathcal{R}^t \stackrel{\Delta}{=} (q_{t - L + L_0 + 1}^R,\ldots,q_{t-1}^R)$, with $\mathcal{R}^t_k = q_{t - L + L_0 + k}^R, k = 1,\ldots,L - L_0 - 1$.  Let $\hat{\Pi}$ denote those policies belonging to $\pi$ with the additional restriction that the new orders $q_t^R, q_t^E$ are measurable functions of only $\hat{I}_t, \mathcal{R}^t$.  More formally, $\pi \in \hat{\Pi}$ if there exists a sequence of measurable maps $\lbrace \hat{f}^{\pi}_t, t \geq 1 \rbrace$, where each $\hat{f}^{\pi}_t$ is a deterministic measurable function with domain $\Bbb{R}^{L - L_0}$ and range $\Bbb{R}^{+,2}$, s.t. the regular order placed in period $t$ equals $\hat{f}^{\pi}_{R,t}(\mathcal{R}^t,\hat{I}_t)$ and the express order placed in period $t$ equals $\hat{f}^{\pi}_{E,t}(\mathcal{R}^t,\hat{I}_t)$.

Note that $\hat{I}_1 = - \sum_{i=1}^{\hat{G}} D'_{-i}$, and $\mathcal{R}^1 = \mathbf{0}$.  Also, for any policy $\pi \in \hat{\Pi}$ and $t \geq 1$, it holds that $\hat{I}_{t+1} = \hat{I}_t + q_t^E + \mathcal{R}^t_1 - D_t$, $\mathcal{R}^{t+1}_k = \mathcal{R}^t_{k+1}$ for $k \in [1, L - L_0 - 2]$, and $\mathcal{R}^{t+1}_{L - L_0 - 1} = q_t^R$.  Furthermore, for all $t \geq L_0 + 1$, $C^{\pi}_t = G(\hat{I}_{t - L_0} + q_{t - L_0}^E - \sum_{i = t - L_0}^t D_i) + c q_{t - L_0}^E$.  Then the following is proven in \citet{Sheopuri10}.

\begin{lemma}[\citet{Sheopuri10}\ Lemma 2.1]
$\inf_{\pi\in \Pi} C(\pi) =  \inf_{\pi\in \hat{\Pi}} C(\pi)$, i.e. one may w.l.o.g. restrict oneself to policies belonging to $\hat{\Pi}$.
\end{lemma}
For the remainder of the paper, we thus consider the relevant optimization only over policies belonging to $\hat{\Pi}$, i.e.
\begin{equation}\label{theprob1}
\textrm{OPT}(L) = \inf_{\pi\in \hat{\Pi}} C(\pi).
\end{equation}

For a given policy $\pi \in \hat{\Pi}$, let $\mathcal{R}^{\pi,t} (\hat{I}^{\pi}_t)$ denote a r.v. distributed as the truncated regular pipeline (expedited inventory position) at the start of period $t$ under policy $\pi$.  Similarly, let $q_t^{\pi,E} (q_t^{\pi,R})$ denote the expedited (regular) order placed in period $t$, and suppose that all these r.v.s are constructed on a common probability space, and have the appropriate joint distribution induced by the operation of $\pi$ over time.

\subsection{TBS policy}\label{ds-sec-TBS}
In this section, we formally introduce the family of TBS policies, and characterize the ``best" TBS policy.  A TBS policy $\pi_{r,S}$ with parameters ($r,S$) is defined (cf. JSS) as the policy that places a constant order $r$ from R in every period, and follows an order-up-to rule from E which in each period raises the expedited inventory position to $S$ (if it is below $S$), and otherwise orders nothing.  More formally, under this policy $q^R_t = r$, and $q^E_t = \max(0, S - \hat{I}_t)$, for all $t$.

Let  $I^r_{\infty} \stackrel{\Delta}{=} \sup_{j \geq 0} \left(j r - \sum_{i=1}^j D_{i}\right)$.  In that case, it follows from the results of JSS that
\begin{equation}\label{TBSformula}
C(\pi_{r,S}) =\ c(\bbe[D] - r)+ \bbe\left[G\left( I^r_{\infty} + S - \sum_{i=1}^{L_0 + 1} D'_i \right)\right].
\end{equation}

Note that for each $r$, the minimization problem $\inf_{S \in \bbr} C(\pi_{r,S})$ is equivalent to a standard one-period newsvendor problem.  Furthermore, defining $F^{\infty}(r) \stackrel{\Delta}{=} \inf_{S \in \bbr} C(\pi_{r,S})$, it is proven in JSS that $F^{\infty}(r)$ is convex in $r$ on $\left(-\infty, \bbe[D]\right)$.  Combining the above with standard results for single-server queues (cf. \citet{Asmussen03}) and (\ref{Lip1}), we conclude that there exists at least one pair ($r^*, S^*$) s.t. $r^* \in \argmin_{0\leq r\leq \E[D]} F^{\infty}(r)$ and $S^* \in \argmin_{S \in \bbr} C(\pi_{r^*,S})$; that this pair defines the TBS policy with least long-run-average cost; and that this pair can be computed efficiently by solving a convex program which is independent of the larger lead time $L$.

\subsection{Main result}\label{ds-sec-main}
\subsection{Additional definitions and notations}
Before stating our main result, we will need several additional definitions and notations to describe various relevant quantities which will appear in our bounds on the optimality gap.  For $\theta \geq 0$ and $\epsilon \in \big(0,\E[D]\big]$, let us define
$$\phi_{\epsilon}(\theta) \stackrel{\Delta}{=} \exp\big(\theta (\E[D] - \epsilon)\big) \bbe[\exp(- \theta D)]\ \ \ ,\ \ \ \gamma_{\epsilon} \stackrel{\Delta}{=} \inf_{\theta \geq 0} \phi_{\epsilon}(\theta),$$
and $\vartheta_{\epsilon} \in \argmin_{\theta \geq 0} \phi_{\epsilon}(\theta)$ denote the supremum of the set of minimizers of $\phi_{\epsilon}(\theta)$,
where we define $\vartheta_{\epsilon}$ to equal $\infty$ if the above infimum is not actually attained.  Note that $\phi_{\epsilon}(\theta)$ is a continuous and convex function of $\theta$ on $(0,\infty)$, and right-continuous function of $\theta$ at $0$.
In addition, it follows from \cite{Folland99} Theorem 2.27 that $\phi_{\epsilon}(\theta)$ is right-differentiable at zero, with derivative equal to $- \epsilon$.  We conclude from the definition of derivative and a straightforward contradiction argument that $\vartheta_{\epsilon} > 0$ and $\gamma_{\epsilon} \in [0,1)$.  Let $g \stackrel{\Delta}{=} \inf_{x \in \Bbb{R}} \bbe\left[G\left( x - \sum_{i=1}^{L_0 + 1} D'_i \right)\right] > 0$, and $U \stackrel{\Delta}{=} C(\pi_{0,0}) = c \E[D] + \E[G(- \sum_{i=1}^{L_0 + 1} D'_i)]$, in which case it is easily verified that $g \leq \textrm{OPT}(L) \leq U$ for all $L > L_0 + 1$.  We also make the following additional definitions:
$$p_0 \stackrel{\Delta}{=} \p(D < \E[D]) \in (0,1)\ \ \ ,\ \ \ \hat{p}_0 \stackrel{\Delta}{=} \big(\frac{1}{2} p_0 (1 - p_0)\big)^{\frac{1}{2}} \in (0,1)\ \ \ ,\ \ \ Q_0 \stackrel{\Delta}{=} \inf\lbrace x \in \Bbb{R}^+: \p(D \leq x) \geq \frac{1}{2} p_0 \rbrace \in [0,\E[D]),$$
$$\eta_0 \stackrel{\Delta}{=} \inf_{z \in \Bbb{R}} \E[|z - D|] > 0\ \ \ ,\ \ \ c_0 \stackrel{\Delta}{=} \frac{1}{240} \min(b,h) \hat{p}_0 \eta_0\ \ \ ,\ \ \ U_0 \stackrel{\Delta}{=} 64 (L_0 + 1) \frac{\max^2(b,h)}{\min(b,h)} \E[D],$$
$$\epsilon_0 \stackrel{\Delta}{=} \min\bigg(\E[D] - Q_0 , \frac{1}{4}(\eta_0 \hat{p}_0)^2 , 1 - 2^{-\frac{\hat{p}^2_0}{400}} , \frac{1}{625} c^2_0 \big( U_0 2^{L_0} + \eta_0 + U + 1\big)^{-2} \bigg) \in (0,1 - 2^{-\frac{1}{400}}) \subset (0 , .002),$$
$$Y_0 \stackrel{\Delta}{=} 25 g^{-2}  \big( U_0 2^{L_0} +  \max(b,h) \gamma_{\epsilon_0} \vartheta^{-1}_{\epsilon_0}(1 - \gamma_{\epsilon_0})^{-2} \big)^2 + L_0 + 1.$$
Our main result proves that the best TBS policy is asymptotically optimal as $L\to \infty$, and provides explicit bounds on the optimality gap.
\begin{theorem}\label{ds-thm-main1}
For all $L_0 \geq 0$, $\epsilon \in (0,1)$, and $L > \epsilon_0^{-2} + Y_0 \epsilon^{-2}$, it holds that $\frac{C(\pi_{r^*,S^*})}{\textrm{OPT}(L)} < 1 + \epsilon$.
\end{theorem}
\begin{corollary}\label{maincorr11}
$\lim_{L\to \infty} \frac{C(\pi_{r^*,S^*})}{\textrm{OPT}(L)} = 1.$
\end{corollary}
\section{Proof of Theorem \ref{ds-thm-main1}}\label{ds-sec-proof}
\subsection{Lower bound for the optimal cost}\label{ds-sec-lower}
In this section, we prove a lower bound for $\textrm{OPT}(L)$ by extending the steady-state/convexity approach of \citet{Xin14a} to the dual-sourcing setting.  We note that here our lower bound will involve a non-trivial optimization over measurable functions,
in contrast to the bounds used in \citet{Xin14a} which were of a static nature.  As in \cite{Xin14a}, we will proceed by relating the ``long-run behavior" of ``an optimal policy" to a certain TBS policy.  At a high level, we will combine convexity and the conditional Jensen's inequality with the fact that the r.v.s corresponding to (appropriately defined stationary versions of) the different components of the truncated regular pipeline vector (under the optimal policy) have the same mean, which will (approximately) coincide with the constant order from R in our TBS policy.  Furthermore, when we apply the conditional Jensen's inequality to certain terms corresponding to (appropriately defined stationary versions of) the expedited orders under the same optimal policy, the resulting terms will be suitably measurable functions of past demands, which will (approximately) coincide with the amount of inventory ordered from E in our TBS policy.
\subsubsection{Connecting to a stationary problem.}
As in \cite{Xin14a}, our program immediately encounters a technical problem.  Namely, the natural way to analyze the ``long-run behavior" of an optimal policy is through the steady-state distribution of the Markov chain induced by this policy.  However, it is not obvious that this steady-state exists.  Actually, it is not even obvious that there exists a stationary optimal policy (so that the dynamics even define a Markov chain), nor even that there even exists an optimal policy at all (as opposed to it only being approached).  Although such questions have been rigorously analyzed for simpler inventory models in \cite{Huh11}, such questions have not been rigorously answered for the setting of more complicated dual-sourcing models.  We note that although in \cite{Sheopuri10} it is stated in passing that many of the same results should extend to the dual-sourcing setting, no proofs are provided, and the explicit assumptions needed for such a transference are not clarified.  A similarly terse exposition on related questions is provided in \cite{Hua14}.  Furthermore, in none of these works is the question of existence of and convergence to relevant stationary measures discussed.  To overcome this, as in \cite{Xin14a}, we first observe that we will not actually need a random vector which is truly the steady-state of the aforementioned Markov chain (which in principle may not exist), but only need to demonstrate the existence of a random vector which has several properties that we would want such a steady-state (if it existed) to have.  We now show the existence of such a random vector.  We note that although closely related questions have been studied in the MDP literature (cf. \cite{Arapostathis93}), and perturbative approaches similar to the approach we take in our own proof are in general well-known (cf. \cite{Filar}), to the best of our knowledge the desired result does not follow directly from any results appearing in the literature.  As such, we include a proof for completeness in the technical appendix Section\ \ref{techsec}.  We note that here the relevant analysis is considerably more challenging than that given in \cite{Xin14a}, due to the fact that in the dual-sourcing setting the inventory level is unbounded from below, and the associated ordering levels are not known to be uniformly bounded (in contrast to the setting considered in \cite{Xin14a} for which such bounds were already proven in \cite{Zipkina}).  Furthermore, although several bounds exist in the dual-sourcing literature relating order levels under an optimal policy to the inventory level at the time of ordering (cf. \cite{Sheopuri10,Hua14}), it seems that due to the inventory being unbounded below none of those bounds are suitable for our purposes.  It is also worth noting that our approach is able to side-step many of the complexities and additional assumptions (e.g. finite second moment or bounded support) often required when analyzing inventory models which are unbounded from below.
\\\indent We defer all relevant proofs to the technical appendix Section\ \ref{techsec}.  For two r.v.s $X,Y$, let $X \sim Y$ denote equivalence in distribution.  Before stating our result, for the sake of building intuition, we first describe what the various r.v.s appearing in our result would correspond to ``if we were to assume" (which we do not, i.e. it is not an assumption of our main results) that there exists an optimal policy which is stationary, and whose corresponding Markov chain converges to a steady-state distribution, i.e. the truncated regular pipeline and expedited inventory position converge in distribution under the operation of this optimal stationary policy.  In that case, our theorem contains an $(L - L_0 - 1)$-dimensional random vector $\mathbf{\chi}^{*, L}$, an $(L - L_0)$-dimensional random vector $\mathbf{q}^{*,L}$, and a r.v. $\mathcal{I}^{*, L}$, which may be interpreted as follows.  Suppose one has been operating under this stationary optimal policy for a long time, say up to some very large time $T$, at which time the system is essentially in steady-state (again we note that this discussion is purely for the sake of building intuition, and our main results do not actually assume this).  Then $\mathbf{\chi}^{*, L}$ corresponds to the steady-state truncated regular pipeline vector under this optimal policy (at time $T$), i.e. $\mathbf{\chi}^{*, L}_i$ is the regular order which enters the expedited inventory position in period $T + i - 1$.  $\mathbf{q}^{*,L}$ corresponds to the steady-state vector of expedited orders to be placed over the next $L - L_0$ periods under this optimal policy, i.e. $\mathbf{q}^{*, L}_i$ is the expedited order which enters the expedited inventory position in period $T + i - 1$.  Finally, $\mathcal{I}^{*, L}$ corresponds to the steady-state expedited inventory position under this optimal policy (at time $T$).

\begin{theorem}\label{proxychain0}
For all $L_0 \geq 0$ and $L > L_0 + 1$, one may construct  an $L - L_0 - 1$-dimensional random vector $\mathbf{\chi}^{*, L}$, an $L - L_0$-dimensional random vector $\mathbf{q}^{*, L}$, and a random variable $\mathcal{I}^{*, L}$, as well as $\lbrace D_i, i \geq 1 \rbrace$, on a common probability space s.t. the following are true.
\begin{enumerate}[(i)]
\item \label{enum0} W.p.1 $(\mathbf{\chi}^{*, L}, \mathbf{q}^{*, L})$ is non-negative.  Also, $(\mathbf{\chi}^{*, L},\mathcal{I}^{*, L})$ is independent of $\lbrace D_i, i \geq 1 \rbrace$, and $q^{*, L}_i$ is independent of $\lbrace D_j, j \geq i \rbrace$ for $i \in [1, L - L_0]$.
\item \label{enum0b} $\mathbf{\chi}^{*, L}_i \sim \mathbf{\chi}^{*, L}_1$ for $i \in [1 , L - L_0 - 1]$, and $q^{*, L}_i \sim q^{*, L}_1$ for $i \in [1 , L - L_0]$.
\item \label{lseq-300} For all $k \in [1,L - L_0]$,
$$\mathcal{I}^{*, L} + \sum_{i=1}^{k-1} (q^{*, L}_i + \chi^{*, L}_i - D_i) + q^{*, L}_k - \sum_{i = k}^{k + L_0} D_i
\sim \mathcal{I}^{*, L} + q^{*, L}_1 - \sum_{i=1}^{L_0 + 1} D_i.$$
\item \label{enum0mean1}$(\mathbf{\chi}^{*, L}, \mathbf{q}^{*, L},\mathcal{I}^{*, L})$ has finite mean.
\item \label{enum0mean2} $\E[\mathbf{\chi}^{*, L}_1] + \E[q^{*, L}_1] = \E[D]$.
\item \label{enum0mean3} $$\textrm{OPT}(L) \geq c\left(\bbe[D] - \E[\chi^{*, L}_1]\right) + \bbe \left[G\left( \mathcal{I}^{*, L} + q^{*, L}_1 - \sum_{i=1}^{L_0 + 1} D_i\right)\right].$$
\end{enumerate}
\end{theorem}

\subsubsection{Vanishing discount factor approach.}
Although Theorem\ \ref{proxychain0}.(\ref{enum0mean3}) relates $\textrm{OPT}(L)$ to a certain expectation, this expectation (as written) is not immediately amenable to analysis.  To remedy this, we introduce a discount factor $\alpha$ to implement the so-called ``vanishing discount factor" approach to analyzing infinite-horizon MDP (cf. \citet{Huh11}), which will allow for a simpler analysis when we pass to the limit as $L \rightarrow \infty$.  Indeed, this discount factor will help us to analyze the lower bound which arises when we apply the conditional Jensen's inequality, as this lower bound will itself involve the solution to a non-trivial multi-stage dynamic optimization problem.  We note that the lower bound which arose when related techniques were applied to single-sourcing systems with lost sales in \citet{Xin14a} only involved a static optimization problem, and thus no such discount factor was introduced.  In particular, Theorem\ \ref{proxychain0} immediately implies the following corollary.  Let $r_L \stackrel{\Delta}{=} \E[\chi^{*, L}_1]$.

\begin{corollary}\label{proxy00}
For all $L_0 \geq 0, L > L_0 + 1$, and $\alpha \in (0,1)$,
\begin{eqnarray*}
\textrm{OPT}(L) &\geq& c\left(\bbe[D] - r_L\right) + \frac{1-\alpha}{1-\alpha^{L}} \sum_{k=1}^{L} \alpha^{k-1}  \bbe \left[G\left( \mathcal{I}^{*, L} + q^{*, L}_1 - \sum_{i=1}^{L_0 + 1} D_i\right)\right]
\\&\geq& c\left(\bbe[D] - r_L\right) + (1 - \alpha) \sum_{k = 1}^{L - L_0} \alpha^{k - 1}  \bbe \left[G\left(\mathcal{I}^{*, L} + \sum_{i=1}^{k-1} (q^{*, L}_i + \mathbf{\chi}^{* , L}_i - D_i) + q^{*, L}_k - \sum_{i = k}^{k + L_0} D_i\right)\right].
\end{eqnarray*}
\end{corollary}

\subsubsection{Applying the conditional Jensen's inequality and relating to a single-source inventory model.}\label{3pp}
We now apply the conditional Jensen's inequality to Corollary\ \ref{proxy00}, which will allow us to lower-bound $\textrm{OPT}(L)$ by the optimal value of a certain finite-horizon single-source inventory model with backlogged demand.  We will then relate this finite-horizon problem to an associated infinite-horizon problem, which has an optimal stationary policy.  Furthermore, we will connect the behavior of such an optimal stationary policy to the performance of an associated TBS policy, ultimately allowing us to prove our main results.
In particular, it follows from Theorem\ \ref{proxychain0} and the independence structure of the relevant r.v.s that for $k \in [1, L - L_0]$,
$$
\E\bigg[ \mathcal{I}^{*, L} + \sum_{i=1}^{k-1} (q^{*, L}_i + \mathbf{\chi}^{* , L}_i - D_i) + q^{*, L}_k - \sum_{i = k}^{k + L_0} D_i
\bigg| D_{[k + L_0]}\bigg]
$$
equals
$$
\E[\mathcal{I}^{*, L}] + \sum_{i=1}^{k-1} (\E[q^{*, L}_i | D_{[i-1]}] + r_L - D_i) + \E[q^{*, L}_k | D_{[k-1]}] - \sum_{i = k}^{k + L_0} D_i.$$
Further combining with Corollary\ \ref{proxy00}, the convexity of $G$, and Jensen's inequality for conditional expectations, we obtain the following result.
\begin{proposition}\label{OBSuse1}
For any $\alpha\in (0,1)$ and $L> L_0 + 1$, $\textrm{OPT}(L) -  c \left(\bbe[D] - r_L \right)$ is at least
\begin{equation}\label{refer1bb}
\begin{aligned}
& (1 - \alpha) \sum_{k = 1}^{L - L_0} \alpha^{k-1} \bbe\Bigg[G\bigg(
\E[\mathcal{I}^{*, L}] - (L_0 + 1) r_L + \sum_{i=1}^{k-1} \big(\E[q^{*, L}_i | D_{[i-1]}] - (D_i - r_L)\big) \\
&\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \      +\E[q^{*, L}_k | D_{[k-1]}] - \sum_{i = k}^{k + L_0} (D_i - r_L)
\bigg)\Bigg].
\end{aligned}
\end{equation}
\end{proposition}

Note that (\ref{refer1bb}) is the discounted cost incurred (during periods $L_0 + 1,\ldots,L$) by the policy ordering $\E[q^{*, L}_i | D_{[i-1]}]$ in period $i$, of a single-sourcing $L$-period backlog inventory problem with unit holding cost $h$, backorder cost $b$, zero ordering cost, discount factor $\alpha$, i.i.d. demand distributed as $D - r_L$ (which we note can be positive \emph{or negative}), lead time $L_0$, and initial inventory position (initial net inventory plus all entries of the initial pipeline vector) $\E[\mathcal{I}^{*, L}] - (L_0 + 1) r_L$ (cf. \citet{Karlin58}), multiplied by $(1 - \alpha)$.  Such models, and their optimal policies, have been studied in-depth in the literature (cf. \citet{Karlin58, Zipkin00, Fleischmann03}), and are well-understood (especially for the case of non-negative demand, cf. \citet{Zipkin00}).  Let $\overline{\Pi}$ denote the family of all feasible non-anticipative policies for the aforementioned inventory problem (as it is typically defined, cf. \citet{Zipkin00}).  For $\pi \in \overline{\Pi}$, initial inventory position $x \in \bbr$, $r \in \bbr$, and $i \geq 1$, let $C^{\pi}_i(r,x)$ denote the cost incurred by policy $\pi$ in the aforementioned inventory problem in period $i + L_0$, if the demand in each period is i.i.d. distributed as $D - r$ (with the leadtime $L_0$ and costs $b,h$ as above).  For $x \in \bbr, r \in \bbr, \alpha \in (0,1), n \geq 1$, let us define
\begin{equation}\label{ds-finite}
V_{\alpha}^{n}(r,x) \stackrel{\Delta}{=}\ \inf_{\pi\in \overline{\Pi}} \bbe\left[\sum_{i = 1}^n \alpha^{i-1} C^{\pi}_i(r,x)\right];
\end{equation}
and
\begin{equation}\label{ds-infinite}
V_{\alpha}^{\infty}(r,x) \stackrel{\Delta}{=}\ \inf_{\pi\in \overline{\Pi}} \bbe\left[\sum_{ i = 1}^{\infty} \alpha^{i-1} C^{\pi}_i(r,x)\right].
\end{equation}
As a notational convenience, we define $V_{\alpha}^0(r,x) = 0$, $V_{\alpha}^n(r,-\infty) \stackrel{\Delta}{=} \inf_{x \in \bbr} V_{\alpha}^n(r,x), V_{\alpha}^{\infty}(r,-\infty) \stackrel{\Delta}{=} \inf_{x \in \bbr} V_{\alpha}^{\infty}(r,x)$.  Then combining the above, we derive the following lower bound for $\textrm{OPT}(L)$.

\begin{lemma}\label{reduce0}
For all $L_0 \geq 0, L > L_0 + 1$, and $\alpha \in (0,1)$,
\begin{equation}\label{inter1}
\textrm{OPT}(L) \geq c (\bbe[D] - r_L) + (1 - \alpha) V_{\alpha}^{L - L_0}(r_L, -\infty).
\end{equation}
\end{lemma}

\subsubsection{Overview of remainder of the proof of our main results.}

The remainder of the proof involves a careful analysis of the right-hand-side (r.h.s.) of (\ref{inter1}) as $L \rightarrow \infty$, and we now sketch an outline of our approach.  First, we will prove that if $r_L$ is bounded away from $\E[D]$, then
$V_{\alpha}^{\infty}(r_L, -\infty) - V_{\alpha}^{L - L_0}(r_L, -\infty)$ can be suitably bounded by a function of $L$ which converges to 0 as $L \rightarrow \infty$.  We then observe that the infinite-horizon problem associated with $V_{\alpha}^{\infty}(r_L, -\infty)$ has an optimal policy which is stationary, Markov, and of order-up-to type.  Furthermore, the stochastic process induced  by this optimal policy will be equivalent to that induced by a corresponding TBS policy, but possibly initialized \emph{not according to the stationary distribution of the associated inventory process}.  Then we prove that $r_L$ is indeed bounded away from $\E[D]$, since otherwise we can use the theory of random walks to derive a contradiction (as $\textrm{OPT}(L)$ would be strictly greater than $U$).  Finally, we combine these facts to bound various error terms under a suitable choice of $\alpha$ (which converges to 1 as $L \rightarrow \infty$), including a term resulting from the difference between the performance of the same TBS policy under different initializations, to prove our main result Theorem\ \ref{ds-thm-main1}.

\subsection{Proof of Theorem\ \ref{ds-thm-main1}}
We now complete the proof of Theorem\ \ref{ds-thm-main1} by formalizing the argument sketched at the end of Section\ \ref{ds-sec-lower}.  Such arguments are standard in the literature on MDP and infinite-horizon inventory control problems (cf. \citet{Iglehart63, Sennott89, Schal93, Fleischmann03, Feinberg11, Huh11}).  We note that the somewhat non-standard aspect here is that the demand in each period is distributed as $D - r_L$, and thus \emph{may be negative}.  As such, the original arguments typically used to analyze the relevant quantities and prove related interchange-of-limits results (cf. \citet{Iglehart63}) do not directly apply.  The possibility of negative demand also makes the verification of the conditions of general theorems which validate such bounds and interchange-of-limits (cf. \citet{Sennott89,Schal93}) somewhat involved, even when these theorems are customized to the inventory setting (cf. \citet{Parker04, Huh11}).  We note that the verification of closely related results have arisen recently in the context of analyzing inventory systems with returns, which reduce to standard inventory systems where demand can be positive or negative (cf. \citet{Fleischmann03}).  However, those results (which verify the technical conditions of \citet{Sennott89}) do not seem to extend immediately to our case, and further seem to require that the demand and ordering quantities take integer values.  In light of the above, and for the sake of clarity and completeness, we now provide a self-contained proof of all necessary bounds, which (combined with Lemma\ \ref{reduce0}) will complete the proof of our main result Theorem\ \ref{ds-thm-main1}.  We defer most proofs to the technical appendix Section\ \ref{techsec}.

We begin by stating some well-known properties of $V_{\alpha}^{n}(r,x)$ and $V_{\alpha}^{\infty}(r,x)$, which follow from the results of JSS, \citet{Karlin58} and \citet{Scarf60}.  We note that although in some cases the proofs there are only explicitly given for the case of non-negative demand, as noted in \citet{Heyman84} and \citet{Fleischmann03}, the arguments carry over to the general case (in which demand may be negative) with only trivial modification.

\begin{lemma}[JSS, \citet{Scarf60}]\label{use1}
For all $\alpha \in (0,1), r, x \in \bbr$, and $n \geq 1$,
$$
V_{\alpha}^{n}(r,x) = \inf_{y \geq x} \left( \bbe\left[G\big(y - \sum_{k=n}^{L_0 + n} (D_k - r) \big)\right] + \alpha \bbe\left[V_{\alpha}^{n-1}\big(r, y - (D_{L_0 + n} - r)\big)\right] \right).$$
Furthermore, $V_{\alpha}^n(r,x)$ is: a convex (and thus also continuous) function of $x$ on $\bbr$ for each fixed $n,r$; a continuous function of $r$ on $\bbr$ for each fixed $n,x$; an increasing function of $x$ on $\bbr$ for each fixed $n,r$; and an increasing function of $n$ on $Z^+$ for each fixed $x,r$.  In addition, the infinite-horizon problem stated in the r.h.s. of (\ref{ds-infinite}) admits an optimal stationary Markov policy.
\end{lemma}

Next, we bound $V_{\alpha}^{\infty}(r,x) - V_{\alpha}^n(r,x)$, and combine our bounds with Lemma\ \ref{use1} to derive some useful properties of $V_{\alpha}^{\infty}(r,x)$ and the associated optimization problem.  We defer all proofs to the technical appendix Section\ \ref{techsec}.  Let $\overline{S}_{\alpha}(r) \stackrel{\Delta}{=} 4 (L_0 + 1) \frac{\max(b,h)}{\min(b,h)}(|r| + \E[D])(1 - \alpha)^{-2}$.

\begin{lemma}\label{limequal2}
For $\alpha \in (0,1)$, $r, x \in \bbr$, and $n \geq 1$,
\begin{equation}\label{limequal2a}
0 \leq  V_{\alpha}^{\infty}(r,x) - V_{\alpha}^n(r,x) \leq \max(b,h) \big(\overline{S}_{\alpha}(r) + |x| + |r| + \E[D]\big) (1 + L_0 + n) (1 - \alpha)^{-2} \alpha^n,
\end{equation}
and $V_{\alpha}^{\infty}(r,x) = \lim_{n \rightarrow \infty} V_{\alpha}^n(r,x)$.  Furthermore, for $\alpha \in (0,1)$ and $r \in \bbr$, $V_{\alpha}^{\infty}(r,x)$ is a finite-valued, convex, and non-decreasing function of $x$ on $\bbr$.  Letting $S_{\alpha}^{\infty}(r)$ denote the supremum of the set of minimizers (in $x$) of $V_{\alpha}^{\infty}(r,x)$, it holds that $|S_{\alpha}^{\infty}(r)| \leq \overline{S}_{\alpha}(r)$, and the infinite-horizon problem stated in the r.h.s. of (\ref{ds-infinite}) admits an optimal stationary base-stock policy, with order-up-to level $S_{\alpha}^{\infty}(r)$.  In addition, for $L_0 \geq 0$, $L > L_0 + 1$, and $\alpha \in (0,1)$,
\begin{equation}\label{limequal2b}
\textrm{OPT}(L) \geq c(\bbe[D] - r_L) + (1 - \alpha) V_{\alpha}^{\infty}\big(r_L, S_{\alpha}^{\infty}(r_L) \big) -  U_0 (1 - \alpha)^{-3} L \alpha^{L - L_0}.
\end{equation}
\end{lemma}

We now formally define the Markov process representing the inventory position process under such an optimal stationary base-stock policy, initialized in state $S_{\alpha}^{\infty}(r_L)$.  Let $S_{\alpha,L} \stackrel{\Delta}{=} S_{\alpha}^{\infty}(r_L)$.  For $r \in [0,\E[D]]$ and $y \in \Bbb{R}$, let $\lbrace X^{r,y}_k, k \geq 1 \rbrace$ denote the following Markov process.  $X^{r,y}_1$ equals $y$.  For all $k \geq 1$, $X^{r,y}_{k+1} = \max\big( X^{r,y}_k + r - D_k, y \big)$.  Let $W^r_k \stackrel{\Delta}{=} \sum_{j=1}^k (r - D_j)$,
$Z^r_k \stackrel{\Delta}{=} \max_{i \in [0,k - 1]} W^r_i$, $Z^r_{\infty} \stackrel{\Delta}{=}  \sup_{i \geq 0} W^r_i$, $M^r_k \stackrel{\Delta}{=} \E[Z^r_k]$, $M^r_{\infty} \stackrel{\Delta}{=} \E[Z^r_{\infty}]$.  It follows from the well-known analysis of the single-server queue using Lindley's recursion (cf. \citet{Asmussen03}) that $X^{r,y}_k \sim y + Z^r_k$; and $X^{r,y}_{\infty} \stackrel{\Delta}{=} \lim_{k \rightarrow \infty} X^{r,y}_{k}$ (in the sense of weak convergence) is a well-defined r.v. distributed as $y + Z^r_{\infty}$.

Combining these definitions with Lemmas\ \ref{use1} and\ \ref{limequal2}, we conclude the following.

\begin{corollary}\label{wrapit0}
For $L_0 \geq 0, L > L_0 + 1$, and $\alpha \in (0,1)$,
$$
\textrm{OPT}(L) \geq c(\bbe[D] - r_L) + (1 - \alpha) \sum_{k=1}^{\infty} \alpha^{k-1} \E\big[G\big(S_{\alpha,L} + Z^{r_L}_k - \sum_{i=1}^{L_0 + 1} (D'_i - r_L)\big)\big] -  U_0 (1 - \alpha)^{-3} L \alpha^{L - L_0}.
$$
\end{corollary}

We now briefly review some useful properties of $Z^r_k$, which we will use to complete the proof of our main results.  These properties follow by combining generally well-known results for generating functions, large deviations, single-server queues, and recurrent random walks
(cf. \citet{Spitzer56, Kingman62a, Folland99, Asmussen03, Xin14a}), and we omit the details.

\begin{lemma}\label{zreview}
For all $r > 0$, $\lbrace M^r_k, k \geq 1 \rbrace$ is non-decreasing, $M^r_{\infty} = \lim_{k \rightarrow \infty} M^r_k$, and for all $i \geq j \geq 1$, $M^r_i - M^r_j = \sum_{k=j}^{i-1} k^{-1} \E[\max(0,W^r_k)].$
If there exists $\epsilon \in (0, \E[D])$ s.t. $r \leq \E[D] - \epsilon$, then $M^r_{\infty} < \infty$, and $M^r_{\infty} - M^r_{n} \leq \big(\vartheta_{\epsilon}(1 - \gamma_{\epsilon})\big)^{-1} \gamma_{\epsilon}^n$ for all $n \geq 1$.
\end{lemma}

Finally, we will also need the following corollary (of Lemma\ \ref{zreview}), which shows that $r_L$ is uniformly bounded away from $\E[D]$ in an appropriate sense, and whose proof we again defer to the technical appendix Section\ \ref{techsec}.
\begin{corollary}\label{lbound1}
For all $L > \epsilon_0^{-2} + L_0 + 1$, it holds that $r_L < \E[D] - \epsilon_0$.
\end{corollary}

We now complete the proof of our main results.
\proof{Proof of Theorem\ \ref{ds-thm-main1}}
It follows from (\ref{TBSformula}) that for all $\alpha \in (0,1)$,
\begin{eqnarray*}
C(\pi_{r_L,S_{\alpha,L} + (L_0 + 1) r_L}) &=& c (\E[D] - r_L) + \bbe\left[G\left( S_{\alpha,L} + Z^{r_L}_{\infty} + (L_0 + 1) r_L - \sum_{i=1}^{L_0 + 1} D'_i\right)\right]
\\&=& c (\E[D] - r_L) + (1 - \alpha) \sum_{k=1}^{\infty} \alpha^{k-1} \bbe\left[G\left( S_{\alpha,L} + Z^{r_L}_{\infty} -  \sum_{i=1}^{L_0 + 1} (D'_i - r_L) \right)\right].
\end{eqnarray*}
Combining with Corollaries\ \ref{wrapit0} and\ \ref{lbound1}, Lemma\ \ref{zreview}, (\ref{Lip1}), and the fact that $L > \epsilon_0^{-2} + L_0 + 1$, we conclude that for all $\alpha \in (0,1)$, $C(\pi_{r^*,S^*}) - \textrm{OPT}(L) - U_0 (1 - \alpha)^{-3} L \alpha^{L - L_0}$ is at most
\begin{eqnarray*}
\ &\ &\ (1 - \alpha) \sum_{k=1}^{\infty} \alpha^{k-1}
\left(
\bbe\left[G\left(S_{\alpha,L} + Z^{r_L}_{\infty} - \sum_{i=1}^{L_0 + 1} (D'_i - r_L) \right)\right]
-
\E\left[G\left(S_{\alpha,L} + Z^{r_L}_k - \sum_{i=1}^{L_0 + 1} (D'_i - r_L)\right)\right]
\right) \nonumber
\\&\ &\ \ \ \ \ \ \leq\ \ \ \max(b,h) (1 - \alpha) \sum_{k=1}^{\infty} \alpha^{k-1} \big( \vartheta_{\epsilon_0}(1 - \gamma_{\epsilon_0})\big)^{-1} \gamma_{\epsilon_0}^k \nonumber
\\&\ &\ \ \ \ \ \ =\ \ \ \max(b,h) \gamma_{\epsilon_0} \big(\vartheta_{\epsilon_0}(1 - \gamma_{\epsilon_0})\big)^{-1} \frac{1 - \alpha}{1 - \gamma_{\epsilon_0} \alpha} \nonumber
\\&\ &\ \ \ \ \ \ \leq\ \ \ (1 - \alpha) \max(b,h) \gamma_{\epsilon_0} \vartheta^{-1}_{\epsilon_0}(1 - \gamma_{\epsilon_0})^{-2}. \nonumber
\end{eqnarray*}
We conclude that for all $\alpha \in (\frac{1}{2},1)$, $C(\pi_{r^*,S^*}) - \textrm{OPT}(L)$ is at most
$$
U_0 2^{L_0} (1 - \alpha)^{-3} L \alpha^L + (1 - \alpha) \max(b,h) \gamma_{\epsilon_0} \vartheta^{-1}_{\epsilon_0}(1 - \gamma_{\epsilon_0})^{-2}.$$
As $L > \epsilon_0^{-2} + L_0 + 1$ implies $L > 100$, which itself may be shown to imply that $5 \frac{\log(L)}{L} < \frac{1}{2}$, we may set $\alpha = 1 - 5 \frac{\log(L)}{L}$.  Then applying the fact that $1 - \alpha \leq \exp(- \alpha)$, we conclude that
$$C(\pi_{r^*,S^*}) - \textrm{OPT}(L) \leq 5 \frac{\log(L)}{L} \big( U_0 2^{L_0} +  \max(b,h) \gamma_{\epsilon_0} \vartheta^{-1}_{\epsilon_0}(1 - \gamma_{\epsilon_0})^{-2} \big).$$
As $\frac{\log(L)}{L} < L^{-\frac{1}{2}}$ for all $L \geq 1$, combining with the fact that $\textrm{OPT} \geq g$ and a straightforward calculation completes the proof.  $\Halmos$.
\endproof

\section{Conclusion}\label{ds-sec-conclusion}
In this paper, we proved that when the lead time of the express source is held fixed, a simple TBS policy is asymptotically optimal for the dual-sourcing inventory problem as the lead time of the regular source grows large.   Our results provide a solid theoretical foundation for several conjectures and numerical experiments appearing previously in the literature regarding the good empirical performance of such policies.   Furthermore, the simple TBS policy performs nearly optimally exactly when standard DP-based methodologies become intractable due to the curse of dimensionality.  In addition, since the ``best" TBS policy can be computed by solving a convex program that does not depend on the lead time of the regular source, and is easy to implement, our results lead directly to very efficient algorithms with asymptotically optimal performance guarantees.  We also explicitly bound the optimality gap of the TBS policy for any fixed lead time (of the regular source), and prove that this decays inverse-polynomially in the lead time of the regular source.  Perhaps most importantly, since many companies are already implementing such TBS policies, our results provide strong theoretical support for the widespread use of TBS policies in practice.

This work leaves many interesting directions for future research.  First, it would be interesting to further investigate the rate of convergence to optimality of TBS policies as the lead time grows large, especially in light of their use in practical settings.  Although we have not optimized the explicit bounds which we have proven on the optimality gap, we suspect that proving significantly stronger (e.g. exponentially decaying) bounds will require the development of new techniques.  For example, when we apply the conditional Jensen's inequality to lower bound the optimal value by a certain single-sourcing problem in Section\ \ref{3pp}, our current approach does not incorporate the fact that $\E[q^{*, L}_i]$ is the same for all $i$, instead only using the fact that $\E[q^{*, L}_i | D_{[i-1]}]$ is a measurable function of $D_{[i-1]}$.  It seems plausible that incorporating this ``stationary expectations" property may be a promising approach here.  Previous bounds from the literature on the rate of convergence of finite horizon inventory optimization problems to their infinite horizon counterparts, e.g. \citet{Hordijk74,Hordijk75}, may also be helpful.

Second, and related to the aforementioned discussion as regards the rate of convergence to optimality of TBS policies, it would be interesting to identify other more sophisticated algorithms which perform better for small-to-moderate lead times, yet remain efficient to implement.  Indeed, it remains an interesting open question to better understand the trade-off between algorithmic run-time and acheivable performance guarantees in this context, i.e. how complex an algorithm is required to ``exploit" the weak correlations which persist even as the lead time grows large.  In the context of dual-sourcing, potential algorithms here include: the so-called dual-sourcing smoothing policies recently studied in \citet{Boute14}; affine policies more generally (cf. \citet{Bertsimas10}), of which dual-sourcing smoothing policies are a special case; the single index and dual index policies discussed earlier; or the dual-balancing policies analyzed in \citet{Levi08}.  It would also be quite interesting to analyze ``hybrid" algorithms, which could e.g. solve a large dynamic program when the lead time is small, and gradually transition to using simpler heuristics as the lead time grows large; or combine different heuristics depending on the specific problem parameters.  In the context of the above conversation on optimality gaps, we do remind the reader that for any fixed regular lead time a TBS policy is not exactly optimal except in some very special cases (cf. JSS), and that our results (and associated insights) should always be applied with care.

On a final note, combined with the results of \citet{Goldberg12} and \citet{Xin14a}, our methodology lays the foundations for a completely new approach to analyzing inventory models with large lead times.  So far, this approach has been successful in yielding key insights and efficient algorithms for two settings previously believed intractable: lost sales models with large lead times, and dual-sourcing models with large lead time gap.  We believe that our techniques have the potential to make similar progress on many other difficult supply chain optimization problems of practical relevance in which there is a lag between when policy decisions are made and when those decisions are implemented.  This includes both more realistic variants of the lost-sales and dual-sourcing models considered so far (e.g. models with distributional dependencies, parameter uncertainty, complex network structure, and more accurate modeling of costs), as well as fundamentally different models (e.g. inventory systems with remanufacturing when the manufactured and remanufactured lead times differ, cf. \citet{Zhou11}; multi-echelon systems with lost sales and positive lead times, cf. \citet{Huh10}; or models with perishable goods).  In closing, we note that our approach can more generally be viewed as a methodology to formalize the notion that when there is a high level of uncertainty and randomness in one's supply chain, even simple policies perform nearly as well as very sophisticated policies, since no algorithm can ``beat the noise".  Exploring this concept from a broader perspective may be fruitful in yielding novel algorithms and insights for a multitude of problems in operations management and operations research.

\bibliographystyle{nonumber}

redpajama_set_name: RedPajamaArXiv


According to an NBC/Wall Street Journal poll, President Trump has a net favorability rating of negative 4 points, while House minority leader Nancy Pelosi has a net rating of negative 25.
The survey, released Sunday, found that 43 percent surveyed view the president positively or somewhat positively, while 47 percent see him in a negative or somewhat negative light.
However, only 19 percent view Pelosi positively or somewhat positively, while 44 percent view her negatively or somewhat negatively. Pelosi is currently viewed 6 times more negatively than the President.
Keep crying about how terrible Donald Trump is, Pelosi. Clearly, the American people don't think he's as bad as you are.


text:
package org.openuap.cms.keywords.manager.impl;

import java.util.List;

import org.openuap.base.util.QueryInfo;
import org.openuap.base.util.context.PageBuilder;
import org.openuap.cms.keywords.dao.KeywordsDao;
import org.openuap.cms.keywords.manager.KeywordsManager;
import org.openuap.cms.keywords.model.Keywords;

/**
 *

 * 关键词管理实现.
 *

 *
 *

 * $Id: KeywordsManagerImpl.java 4086 2012-11-26 04:25:05Z orangeforjava $
 *

 *
 * @author Joseph
 * @version 4.0
 */
public class KeywordsManagerImpl implements KeywordsManager {
	private KeywordsDao dao;

	public int addKeywords(Keywords keywords) {
		return dao.addKeywords(keywords);
	}

	public void deleteKeywords(Keywords keywords) {
		dao.deleteKeywords(keywords);
	}

	public void deleteKeywordsById(int id) {
		dao.deleteKeywordsById(id);
	}

	public List findAll() {
		return dao.findAll();
	}

	public List getKeywords(QueryInfo qi, PageBuilder pb) {
		return dao.getKeywords(qi, pb);
	}

	public Keywords getKeywordsById(int id) {
		return dao.getKeywordsById(id);
	}

	public List getKeywordsByScope(String scope) {
		return dao.getKeywordsByScope(scope);
	}

	public List getKeywordsByScope(String scope, int status) {
		return dao.getKeywordsByScope(scope, status);
	}

	public void saveKeywords(Keywords keywords) {
		dao.saveKeywords(keywords);

	}

	public void setDao(KeywordsDao dao) {
		this.dao = dao;
	}

}

redpajama_set_name: RedPajamaGithub


The staff of the SEC's Division of Corporation Finance has issued no-action relief that allows an initial coin offering without registration. The no-action relief relies on an opinion of counsel that the underlying digital tokens are not securities as well as several other conditions including (i) the sponsor will not further develop the platform, (ii) the tokens will be immediately useable and functional, and (iii) the tokens are not marketed in a manner that emphasizes their potential for increased market value. In a companion release, the SEC Strategic Hub for Innovation and Financial Technology (FinHub) issued guidance about how to determine if an ICO is an offering of securities under the applicable Howey test. FinHub relies heavily on whether the sponsor of the network will engage in further development of the network or digital asset so as to generate increased market value for investors.
Up until now, the SEC has taken the position that ICOs are securities offerings, subject to the Securities Act's registration and disclosure requirements. This no-action letter and companion guidance suggest that the SEC may back off its aggressive position and allow the digital token world to evolve organically. What is unclear is whether any ICO sponsor should go forward without a no-action letter.
A federal judge has ruled that an initial coin offering may not constitute an offering of securities. In rejecting the SEC's request for a preliminary injunction against an ICO, Judge Gonzalo Curiel of the Southern District of California, opined that the SEC failed to present sufficient facts to satisfy the Howey test requiring an investment of money in a common enterprise with an expectation of profit produced by the efforts of others. Faced with conflicting interpretations of how the ICO operated, the Court denied the preliminary injunction because of genuine disputes about material facts.
The significance of this decision is that a court is requiring the SEC to factually prove the three prongs of the Howey test rather than simply accept the SEC's position that digital tokens are securities. If the SEC fails to prove its case and digital tokens are not securities, the SEC will not have the legal authority to regulate ICOs.
The SEC ordered two initial coin offerings to offer investors rescission and pay a $250,000 fine for failing to register the offerings under the securities laws. These cases represent the first time that the SEC has imposed civil penalties solely for ICO securities offering registration violations. One of the respondents raised $15 million by selling digital tokens intended to create a new digital coin ecosystem related to advertising and mobile phones. The other respondent raised $12 Million to create a blockchain technology for the emerging cannabis industry. The SEC maintains that the digital tokens are "securities" under the Howey test and, therefore, the offerings violated the registration requirements of the 1933 and 1934 Acts. Both respondents undertook to register the offerings.
Given the SEC's concerns about disclosure and compliance for ICOs, it will be interesting to see the extent of disclosure required in the promised registration statements.
Back in January, the SEC raised several regulatory questions around ICO offerings and notified the industry that it would not approve crypto-offerings until the issues were adequately addressed. Any efforts to suggest otherwise will draw the attention of the Enforcement Division's Crypto Unit.
The manager of a crypto hedge fund offered its investors rescission and agreed to pay a $200,000 fine for failing to comply with the securities. The SEC argues that the fund, which invested in digital assets, was "engaged in the business of investing, holding, and trading certain digital assets that were investment securities." Consequently, the offering, which did not comply with Regulation D's private offering safe harbors, should have been registered under the Investment Company Act. The SEC charges violations of the registration provisions of the Securities Act and the Investment Company Act as well as the antifraud rules. This case is the SEC's first enforcement action against a crypto hedge fund manager for failing to register under the Investment Company Act.
OUR TAKE: Most significant is the SEC Enforcement Division taking the position that a fund that invests in digital assets is subject to the securities laws. It remains to be seen whether others will challenge that position in the courts.
Bridget Garcia of Cipperman Compliance Services recently attended the Futures Industry Association Law and Compliance Conference in Washington. The well-attended event addressed cryptocurrencies and related regulation, a major issue of interest to the industry. Panels discussed the evolution and purpose of cryptocurrencies and how the CFTC, SEC and FINRA will carve up regulatory responsibilities. Moving onto more tactical matters, one panel discussed regulatory hot topics, including AML and GDPR, and another panel tackled CCO responsibilities. Day 3 focused heavily on swaps and derivatives. Feel free to contact Bridget if you want more information.
The SEC's Director of Corporation Finance, William Hinman, recently opined that cryptocurrencies themselves are not securities subject to SEC oversight, although undertakings operated by a central control group and targeted to passive third parties would constitute a securities offering. Absent a "central enterprise" such that the digital asset is sold only to be used to purchase a good or service available through the network on which it was created, Mr. Hinman would not apply the securities laws. Factors that transform an enterprise into an offering of securities include (i) a central group that promotes the offering and benefits and expends assets/effort to increase the value; (ii) the raising of funds in excess of what is necessary to establish a functional network; (iii) purchasers that seek a return in excess of the current market value; and (iv) a sales effort directed to the general public rather than users. Mr. Hinman announced that the Division would be willing to offer promoters more formal interpretive or no-action guidance to ensure legal comfort.
OUR TAKE: Mr. Hinman offers practical guidance and some clarity on how to apply decades-old precedent to modern cryptocurrency networks and offerings. We expect more guidance in the coming months from the other SEC divisions.
Last week, the SEC's Division of Investment Management asked sponsors to refrain from initiating registrations for funds investing in cryptocurrencies and related products. Dalia Blass, the Division Director, cited "significant outstanding questions" about how such funds could comply with applicable laws and regulations. In today's Friday List, we describe the top 10 regulatory concerns raised by the Division of Investment Management. Despite these concerns, we believe that the SEC and the industry will work through these issues and develop rules and best practices that will ensure the growth of this market in a manner that engenders investor confidence.
Valuation: The SEC asks whether funds could obtain sufficient information to properly value fund assets pursuant to current accounting rules especially given the "nascent state and current trading volume" in the futures markets.
Liquidity: Could funds reduce crypto-assets to cash so as to meet daily redemption requests? How would funds classify assets under the SEC's new liquidity rule (22e-4)?
Custody: The SEC questions how a fund custodian could validate the existence and ownership of cryptocurrency assets, and how funds would address physical security where applicable.
ETF Creation: Will the creation unit process operate in a way that ensures that funds and authorized participants limit arbitrage opportunities that harm investors?
Volatility: The limited history and volume of the cryptocurrency markets could negatively impact fund operations and affect investors.
Lack of regulation: Neither cryptocurrency markets nor providers/issuers are subject to prudential regulation.
Market manipulation: The SEC cites Chairman Clayton's concerns over market manipulation and potential fraud.
Cybersecurity: Could a potential hack threaten ownership interests and valuation? What safeguards are in place?
Disclosure: How would fund sponsors ensure sufficient risk disclosure and transparency in fund prospectuses and other shareholder communications?
Suitability: How will broker-dealers and advisers ensure their suitability and fiduciary obligations when recommending crypto-funds to retail investors?
OUR TAKE: We believe that both the industry and the SEC have vested interests in coming to an agreement to allow cryptocurrency offerings. The industry should welcome prudent regulation, which gives investors the type of confidence that made mutual funds so successful. The SEC should get out in front of this issue to become the regulator of choice rather than cede its regulatory authority to offshore, non-U.S., and private markets.
OUR TAKE: We predicted (not very long ago) that the regulators will pursue regulation of cryptocurrency offerings. This may not be bad for this emerging industry in the long term. After all, significant regulation made mutual funds the most popular investment vehicle of the last 100 years.


remarriage are pretty easy to determine, cohabitation is not.
living together; (2) of a sustained duration; and (3) with shared day-to-day expenses.
Cohabitation is often described as an issue of lifestyle, not a housing arrangement.
and, most often, not worth the time and expense associated with trying to prove it.
There is a change in legal custody of the child.
the support cannot continue past the age of 19.
Enforcement Agency of any reason why a child support obligation should terminate.
can be avoided by a simple phone call.
attorney at the start of your case.
Any other factor the court deems relevant and equitable.
be appropriate. The court has the authority to award both temporary and permanent spousal support.
example, spousal support may be modified in the event that one party loses his or her job.
Denise M. Cook Co., LPA is a law firm focusing on the complex legal issues facing families today. Located in Northeast Ohio covering Cuyahoga, Geauga, Summit, Lake, Portage, and Medina counties.
Disclaimer: The information contained in this website is not, nor is it intended to be, legal advice. You should consult an attorney for advice regarding your individual situation. While your contact and calls are welcome, contact does not create an attorney-client relationship. Please do not send any confidential information until such time as an attorney-client relationship has been established.


text:
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Alpha-thalassemia-myelodysplastic syndrome
Disease definition
An acquired form of alpha-thalassemia characterized by a myelodysplastic syndrome (MDS) or more rarely a myeloproliferative disease (MPD) associated with hemoglobin H disease (HbH).
Synonym(s):
ATMDS
Acquired HbH disease
Acquired hemoglobin H disease
Prevalence: <1 / 1 000 000
Inheritance: Not applicable
Age of onset: Adult
ICD-10: D46.7 D56.0
UMLS: C0585216
About 80 cases have been identified to date and most involved patients are of northern European descent. Some cases have been reported in patients from Asia and the Mediterranean area.
Clinical description
ATMDS occurs predominantly in males during the 7th decade of life (male-to-female ratio greater than 6:1). The main clinical features include anemia and other signs associated with MDS such as shortness of breath, weakness, tendency to bruise or bleed and an increased susceptibility to infections. It has occasionally been associated with MPD and in these cases, splenomegaly frequently co-occurs. MDS progresses to leukemia in about 25% of cases and HbH is usually no longer detectable at this time.
ATMDS is due to acquired somatic mutations in the ATRX gene (Xq21.1). There is also evidence that acquired deletions of chromosome 16p may be causative. These defects result in significant down-regulation of alpha-globin gene expression.
Diagnostic methods
Typical hematological findings show hypochromic microcytic red blood cells and striking anisopoikilocytosis, and the presence of HbH inclusions in a proportion of red blood cells that varies depending on the patients. Cytological and cytogenetic analysis of bone marrow cells is required to confirm the diagnosis and to classify the underlying MDS. Direct sequencing of the ATRX gene in DNA samples from blood or bone marrow usually indicates a mosaicism, identified by a single nucleotide mutation.
Differential diagnoses include other causes of anemia, cytopenia or microcytosis. It is especially important to exclude an inherited form of alpha-thalassemia by molecular analysis of the HBA locus.
Management and treatment
Treatment depends on the underlying MDS. Stem cell transplantation is the only curative treatment but it is rarely feasible. Other treatment options may include hypomethylant (azacitabine) therapy and lenalinomide. Supportive care includes blood transfusions, erythropoietin stimulating agents, growth factors, antibiotics (if infections are present), and iron chelation therapy in those undergoing long term transfusion therapy.
Prognosis depends on the sub-type of MDS according to the International scoring system (ISS). The scoring system takes into account the percentage of marrow blasts, the severity of cytopenia, and cytogenetic analysis of bone marrow cells. Death is usually due to leukemic transformation, infections due to neutropenia, bleeding related to thrombocytopenia and, in some cases, to other co-morbidities such as cardiovascular disease.
Expert reviewer(s): Dr Catherine BADENS - Pr Christian ROSE - Last update: February 2013
Polski (2013, pdf)
Further information on this disease
Classification(s) (3)
Gene(s) (1)
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text:
Kay Morgan-Israel
Kay Morgan-Israel is an award winning singer-songwriter and musician who has a heart for leading people into intimate worship.
Kay began singing in her hometown in Wales when she was just 17. When kay was 27, she gave her life to Jesus and began getting involved in worship teams.
Since then Kay has been writing worship songs and currently tours around the UK with her Songs Of Heaven tour, offering evenings of song ministry and worship to many churches around the country. She also brings the prophetic song, and encourages congregations into more spontaneous worship. She also has a great desire to be part of revival prayer/worship events.
Kay received an award at the Praisetek Gospel Music Awards 2016, in recognition of her contribution towards worship music. Kay is currently working on her debut album.
Kay is available to come to your church for worship evenings, special celebrations and prayer/worship events.
"Kay has a great personality and she is a passionate Praise & Worship singer. It has been a huge blessing to have her at our event. She is very talented, gifted in this area and her music reflects her special love for God. One of the songs she wrote specifically for our event and sang was very blessed. God was there and we were all blessed! May God continue to perfect her gift and use her in Jesus name." Patricia Wagner, Event Organiser.
Kay Morgan-Israel, My Eyes Have Seen The King


Acupuncture is an alternative and complementary medicine used throughout the World to treat various chronic disorders including diabetes. The aim of this present study is to explain the hypoglycemic effect of non-invasive stimulation with Acu-TENS at bilateral Zusanli (ST36) acupoints in Streptozotocin(45 mg /kg / body weight / IP) induced diabetic rats. The Acu - TENS therapy was given with low frequency 15 HZ, high intensity and width of 5 sec pulse at the Zusanli(ST36) acupoints in diabetic induced rats for 5 minutes every day without anaesthesia for 60 days. A more steady significant (p ≤ 0.01) decrease in fasting blood glucose level was noted in Zusanli acupoints treated diabetic rats and compared with antidiabetic drug (pioglitazone,7.5 mg / kg /body weight) treated rats.The acupuncture treated diabetic rats showed more significant (p ≤ 0.01) decrease in total cholesterol, triglycerides, low density lipid and significant increase in high density lipid.Histopathological examination of pancreas in Zusanli acupoints treated diabetic rats showed near normal architecture and regular shaped islets with regeneration of cells and compared with anti-diabetic drug treated rats pancreas. Stimulation at ST36 acupoints produced antidiabetic effects and improved lipid metabolism may be due to increase in insulin secretion through the mediation of β- endorphin and stimulation of Qi (energy flow) and utilisation of energy due to mild muscle twitching during stimulation.


text:
//---------------------------------------------------------------------------//

//---------------------------------------------------------------------------//
/*!
 * \brief DTK_LibmeshEntityIntegrationRule.cpp
 * \author Stuart R. Slattery
 * \brief libMesh integration rule implementation.
 */
//---------------------------------------------------------------------------//

#include "DTK_LibmeshEntityIntegrationRule.hpp"
#include "DTK_LibmeshHelpers.hpp"

namespace DataTransferKit
{
//---------------------------------------------------------------------------//
// Constructor.
LibmeshEntityIntegrationRule::LibmeshEntityIntegrationRule(
    const libMesh::QuadratureType quadrature_type )
    : d_quad_type( quadrature_type )
{ /* ... */
}

//---------------------------------------------------------------------------//
// Given an entity and an integration order, get its integration rule.
void LibmeshEntityIntegrationRule::getIntegrationRule(
    const Entity &entity, const int order,
    Teuchos::Array<Teuchos::Array<double>> &reference_points,
    Teuchos::Array<double> &weights ) const
{
    // Create a libmesh quadrature rule. Use Gauss quadrature as the default.
    libMesh::UniquePtr<libMesh::QBase> libmesh_quadrature =
        libMesh::QBase::build( d_quad_type, entity.topologicalDimension(),
                               static_cast<libMesh::Order>( order ) );

    // Initialize the quadrature rule for the entity.
    Teuchos::Ptr<libMesh::Elem> libmesh_elem =
        LibmeshHelpers::extractGeom<libMesh::Elem>( entity );
    libmesh_quadrature->init( libmesh_elem->type() );

    // Extract the data for the quadrature rule.
    int num_points = libmesh_quadrature->n_points();
    int quad_dim = libmesh_quadrature->get_dim();
    reference_points.resize( num_points );
    weights.resize( num_points );
    for ( int p = 0; p < num_points; ++p )
    {
        weights[p] = libmesh_quadrature->w( p );
        libMesh::Point qp = libmesh_quadrature->qp( p );
        reference_points[p].resize( quad_dim );
        for ( int d = 0; d < quad_dim; ++d )
        {
            reference_points[p][d] = qp( d );
        }
    }
}

//---------------------------------------------------------------------------//

} // end namespace DataTransferKit

//---------------------------------------------------------------------------//
// end DTK_LibmeshEntityIntegrationRule.hpp
//---------------------------------------------------------------------------//


This statement was originally published on hrw.org on 16 October 2015.
Kazakhstan officials have arrested two activists while investigating them on vague and overbroad charges of "inciting national discord," Human Rights Watch said today. An Almaty court confirmed a two-month pretrial detention order on October 15, 2015.
Police arrested Ermek Narymbaev, a civic activist, and Serikzhan Mambetalin, former head of the Rukhaniyat party, on October 12, after receiving information that "they had circulated material on social media that contains clear signs of inciting national discord [and] insulting national honor and dignity," according to a police statement. Kazakh authorities should release them immediately.
Both Narymbaev and Mambetalin are critical of the government and are quite active on social media networks. Both have previously found themselves in government crosshairs for peaceful civic activity. Authorities jailed Narymbaev twice this year for up to 20 days after he attempted to stage peaceful protests. In late 2011, Mambetalin's party was prevented from participating in 2012 parliamentary elections due to alleged irregularities in its party list.
The charges appear to be connected to Narymbaev and Mambetalin's recent Facebook posts about writings attributed to another activist, Murat Telibekov.
Telibekov is the author of a collection of poems and plays that he tried – unsuccessfully – to publish about 20 years ago. Recently, texts that were attributed to Telibekov's book, but that he said he did not write, were posted on the Web. These additional texts, which describe the Kazakh nation in provocative terms, were the subject of Narymbaev's and Mambetalin's Facebook posts.
On October 12, about a dozen police officers detained Narymbaev and searched his office and home, confiscating laptops and modems. The police did not permit Zhanara Balgabaeva, Narymbaev's lawyer, who arrived at his office after the search began, to enter during the search, although she was present during the search of her client's home.
The same day, another group of police officers detained Mambetalin at his home and searched the premises. A family member who was there told Human Rights Watch that the police read the search warrant aloud but did not provide a copy. The police confiscated Mambetalin's computer, tablet, and mobile phone.
Both Balgabaeva and Mambetalin's lawyer, Ermurat Mukanov, told Human Rights Watch that they will appeal the court's decision to place the activists in custody during the investigation period.
Human Rights Watch and others, including the United Nations Special Rapporteur on the rights to freedom of peaceful assembly and of association after his visit to Kazakhstan this year, have called on the Kazakh government to amend the charge of "inciting social, national, clan, racial, class, or religious discord" so that it is strictly and narrowly defined.
In 2014, the Kazakh government broadened the scope of the offense, increasing maximum sentences from 12 years in prison to 20, showing blatant disregard for its obligations under international human rights law.
The offense is so vague and overbroad that it can be, and has been, used to criminalize lawful behavior protected by human rights law. Freedom of opinion, expression, and association are basic rights protected by international treaties to which Kazakhstan is party and should not be violated, Human Rights Watch said.
Earlier that day, Toregozhena had put up a post on Facebook urging those who support Narymbaev and Mambetalin to post excerpts from Telibekov's book.
Telibekov told Human Rights Watch that he did not write the excerpts in question and that they were not included in his original book. He denies having anything to do with posting the book online.
Kazakhstan's international partners, including the United States, the United Kingdom, and European Union member states, should urge the Kazakh government to amend the offense of "inciting social and other discord" without further delay, Human Rights Watch said.
"People in Kazakhstan should be free to debate matters of public interest online and not be worried that they'll land up in jail for expressing an opinion," Rittmann said.


text:
Q: Retornar a página anterior após o login no facebook oauth Uso o sistema de Login pelo facebook padrão, nele pede pra inserir App ID o App Secret e a URL que irá retornar após solicitar o login ao usuário, minha duvida é, como fazer para retornar a url no qual foi solicitado o login. em varias páginas estará o botão de Login, então gostaria que retornasse a página de origem. Como faço?

A: Se você estiver gerando o link de login via php é só mudá-lo dinamicamente.
Por exemplo, na página de notícias fica:
$helper = new FacebookRedirectLoginHelper('http://seusite/noticia.php');
$loginUrl = $helper->getLoginUrl();
...

e nela mesmo pra receber/verificar o usuário de volta fica:
if ( !empty($_GET['code']) ){
...
$helper = new FacebookRedirectLoginHelper('http://seusite/noticia.php');
try {
  $session = $helper->getSessionFromRedirect();
} catch
...

* quando o facebook retorna do login ele traz essa variável GET
Obs.: Na verdade esse segundo trecho de código que coloquei deve vir antes do primeiro. Caso tenha $_GET['code'] ( e/ou uma variável de sessão que você vai usar para guardar o token do login) efetua o login, caso não, gera o link de login (o link que vai ter no botão)

redpajama_set_name: RedPajamaStackExchange


text:
Q: Проблема при загрузке изображений из папки DCIM в Android Доброго времени суток!
Есть класс при помощи которого считываются данные из папок в частном случае DCIM
fun loadPhoto(directory: String): List<String> {
    val dir = Environment.getExternalStoragePublicDirectory(directory)
    val photos: MutableList<String> = ArrayList()
    if (dir != null && dir.isDirectory) {
        val images = dir.listFiles()
        if (images != null) {
            for (image in images) {
                if (image.isDirectory) {
                    loadPhoto(image.absolutePath)
                } else {
                    photos.add(image.absolutePath)
                }
            }
        }
    }
    return photos
}

Путь к папке задается при помощи
Environment.DIRECTORY_DCIM

Файлы в папке имеются. Но во время выполнения при проверке условия выдает NULL.
Если же я задаю вручную:
File(Environment.getExternalStoragePublicDirectory((Environment.DIRECTORY_DCIM)),"hello.jpg")

То при тесте имя файла возвращает корректно...
Перерыл кучу различных сайтов, везде решение подобное моему.
В чем может быть проблема у меня?
В манифесте разрешения выставлены
 <uses-permission android:name="android.permission.READ_EXTERNAL_STORAGE" />
 <uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE" />

Всем кто что либо посоветует огромное спасибо

A:
В манифесте разрешения выставлены

Добавить разрешения в манифест != получить их. Эти разрешения ещё нужно запросить у пользователя.


text: Q: Does anyone have a working example of fluid-animation code for the iPhone? I'm looking for a sample iPhone app that includes animated fluids - for example, a fish tank, or glass of water. Is there one available somewhere?