text:
\section{Introduction}
\label{sec:Intro}
Interacting fermions at finite temperature are fundamental to a wide range of chemical and physical phenomena. Examples include ultracold trapped atoms~\cite{Bloch2005, Haller2015, Schneider2012}, electrons in quantum dots~\cite{Ellenberger2006, Yannouleas2007, Li2007} and warm dense matter~\cite{Cytter2019}. Developing simulation methods that accurately describe correlated fermions at various thermodynamic conditions is therefore very desirable~\cite{Wagner2016}.
The path integral (PI) formulation of quantum mechanics~\cite{Feynman2005} is a powerful approach for studying many-body systems at finite temperature. It is based on the observation that the partition function of a quantum system is isomorphic to the partition function of a fictitious, extended classical system~\cite{Chandler1981}. Assuming the quantum particles are distinguishable, each one is represented by a classical ``ring polymer" composed of $P$ replicas of the particle (the ``beads" of the ring polymer) connected by harmonic springs~\cite{Markland2018}. The frequency of the springs is proportional to the temperature and number of beads. The exact quantum result is obtained in the limit $P \rightarrow \infty $. Beads having the same index but representing different particles interact through a scaled interaction potential. The partition function of the fictitious classical system is typically sampled using molecular dynamics (MD)~\cite{Parrinello1984, Markland2018} or Monte Carlo (MC) methods~\cite{Ceperley1995}.

For $N$ indistinguishable particles, bosons or fermions, one must consider all $N!$ particle permutations. As a result, the fictitious classical system is no longer composed of a single ring polymer for each particle. Ring polymer configurations in which particles are connected into longer rings must be included~\cite{Ceperley1995,Lyubartsev1993}, as shown in Fig.~\ref{fig:Perm} in the two-particle case. The number of ring polymer configurations scales exponentially with system size and enumerating them is impractical for more than a few atoms. In Path Integral Monte Carlo (PIMC) simulations this problem is avoided by using MC moves designed to sample particle permutations, as pioneered by Ceperley and coworkers~\cite{Ceperley1995, Pollock1984, Ceperley1986, Pollock1987, Ceperley1992}.
Recently, we showed that the potential and forces required for path integral molecular dynamics (PIMD) simulations for bosons can be evaluated recursively without enumerating or sampling particle permutations~\cite{Hirshberg2019}. The resulting algorithm scales cubically with system size, which has allowed the first PIMD simulations of large bosonic systems to be performed. In this Communication, we show how this method can be extended to obtain thermodynamic properties for fermionic systems.

\begin{figure}
    \centering
    \includegraphics[width=1.0\columnwidth]{Fig_Perm.jpg}
    \caption{Ring polymer configurations for two indistinguishable particles. The permutations of two particles are shown in green and the corresponding cycle notations are shown in red. The ring polymer configurations can be directly inferred from the cycle notation for permutations.}
    \label{fig:Perm}
\end{figure}

In comparison to bosons, fermions present an additional challenge since even and odd sequential particle permutations carry a positive and negative sign, respectively. As a result, direct sampling of fermionic partition functions is problematic, either in MC or MD, since their integrands are not positive definite. One approach to overcome this problem within the framework of PIMC is the fixed node approximation, often referred to as restricted PIMC~\cite{Ceperley1992}. But since the exact nodal surface of the fermionic density matrix is usually unknown, an approximate ansatz is employed, such as the free electrons density matrix~\cite{Brown2013}.
An alternative approach is to simulate the system as if it were composed of bosons and reweight the results according to the sign of each sampled configuration~\cite{Takahashi1984}. However, this procedure leads to the infamous fermionic sign problem - the exponentially slow convergence of expectation values due to delicate cancellation of positive and negative contributions~\cite{DuBois2017}. It was shown by Troyer and Wiese that a general solution to the sign problem  - an algorithm which converges in polynomial time - is ``almost certainly unattainable''~\cite{Troyer2005}. Even if a complete solution is unlikely, it is highly desirable to develop new methods for simulating fermions which may provide avenues for alleviating the sign problem.

Recently, several methods have been proposed to alleviate the sign problem within PIMC, such as configuration PIMC~\cite{Schoof2011} and permutation blocking PIMC~\cite{Dornheim2015}.
In contrast, only a few methods have been proposed to perform fermionic PIMD simulations in general and even fewer studies have addressed the sign problem in this context. Miura and Okazaki proposed to sample the absolute value of the probability density for fermions~\cite{Miura2000}. The potential is obtained from the absolute value of a determinant, which accounts for all particle permutations.  Expectation values for fermions are obtained by reweighting the contribution of different configurations according to the sign of their determinant. However, this method was applied to only three particles and its sign problem was not investigated in detail. Another limitation of this approach is that the potential has an infinite barrier at the nodes of the fermionic probability density, effectively preventing the system from exploring all regions of phase space.
More recently, Runeson et al.~\cite{Runeson2018} have shown that by combining enhanced sampling techniques with PIMD simulations of distinguishable particles, the problem of two electrons in a quantum dot can be solved. However, it is not clear how to extend their work to larger systems.

In this Communication, we propose a different approach to performing PIMD simulations of fermions. We employ our recently developed method for bosonic PIMD~\cite{Hirshberg2019} and reweight the results to obtain fermionic expectation values. The method is applicable to any system for which the bosonic simulation can be performed and naturally avoids the problem of the infinite barriers, since the bosonic probability density is nodeless. However, as in PIMC, the method suffers from the sign problem at low temperatures. We propose a simple approach to alleviate the sign problem based on the Bugoliubov inequality for the free energy~\cite{feynman1972}. This allows us to estimate the energies of fermionic systems at lower temperatures than would otherwise have been possible using PIMD. In the following, we first present the method in detail. Then, we benchmark the new approach against recent fermionic PIMC simulations by Dornheim~\cite{Dornheim2019} for up to $N=7$ electrons in a two-dimensional quantum dot (QD). In Section~\ref{sec:sign}, we propose to use the Bogoliubov inequality to alleviate the sign problem and apply it to a three-electron QDs at low temperatures. The final section presents the conclusions and briefly discusses future directions.

\section{Theory}
\label{sec:Theory}

The Hamiltonian operator for a system of $N$ identical particles of mass $m$, interacting through a potential $\hat{V}$ is

\begin{equation}
\hat{H} = \frac{1}{2m} \sum_{l=1}^N {\bf \hat{p}}^2_l + \hat{V}({\bf r}_1,...,{\bf r}_N).
\label{eq:H}
\end{equation}

The partition function is obtained by taking the trace of the density operator for a thermal state, $Z = Tr\{e^{-\beta \hat{H}}\}$, where $\beta = (k_B T)^{-1}$ is the inverse temperature and $k_B$ is the Boltzmann constant. The path integral expression for the partition function\cite{tuckerman2010} is

\begin{equation}
Z_I \sim \lim_{P\to\infty} \int e^{-\beta U^{(N)}_I} dR_1 ... dR_N,
\label{eq:Z_PI}
\end{equation}
where $I$ represents whether the particles are bosons (B), fermions (F) or distinguishable (D) and $R_l$ represents collectively the coordinates of $P$ replicas of particle $l$,  $ {\bf r}_l^1,..., {\bf r}_l^P$. In practice, $P$ is increased until the desired expectation values are converged. Here we focus on sampling the partition function of Eq.~\ref{eq:Z_PI} using MD simulations.

For distinguishable particles, the potential is given by

\begin{equation}
U_D^{(N)} = \frac{1}{2}m \omega_P^2 \sum_{l=1}^N \sum_{j=1}^P ({\bf r}_l^{j+1} - {\bf r}_l^j)^2 + \frac{1}{P}\sum_{j=1}^P V({\bf r}_1^j,...,{\bf r}_N^j),
\label{eq:VD_PI}
\end{equation}
where $\omega_P=\sqrt{P}/\beta \hbar$ and ${\bf r}_l^{P+1} = {\bf r}_l^1$.  The first and second terms arise from the kinetic and potential energy operators of the quantum system, respectively.
Eq.~\ref{eq:VD_PI} is isomorphic to the partition function of $N$ classical ring polymers, each one composed of $P$ beads which are connected by harmonic springs\cite{Chandler1981}.
Beads $j$ of different ring polymers (representing different quantum particles) interact through a scaled interaction potential.

In order to treat bosons and fermions, the trace should be taken over a properly symmetrized or anti-symmetrized basis, respectively.
Since the potential energy is invariant under permutations of identical particles, only the term arising from the kinetic energy operator is affected.
Each permutation leads to a ring polymer configuration which can be directly inferred from the cycle notation for the permutation, as demonstrated in Fig.~\ref{fig:Perm} for two particles.
Since the number of permutations is $N!$, direct enumeration of all ring-polymer configurations is possible only for very small systems.
We have recently shown that the potential for bosons can be evaluated recursively, avoiding the need to enumerate the exponentially large number of permutations~\cite{Hirshberg2019}.
The algorithm scales cubically with system size, which allowed the first applications of PIMD to large bosonic systems.
It is also possible to combine PIMC for bosons with PIMD for distinguishable particles in a hybrid algorithm~\cite{Walewski2014,Walewski2014a,Uhl2018,Schran2018,Uhl2019} to treat large systems. However, our method is simpler as it treats both distinguishable and indistinguishable particles on equal footing.

Extending our bosonic PIMD approach~\cite{Hirshberg2019} to fermions is achieved by defining the potential as
\begin{equation}
U_{B/F}^{(N)} = -\frac{1}{\beta} \ln W_{B/F}^{(N)} + \frac{1}{P}\sum_{j=1}^P V({\bf r}_1^j,...,{\bf r}_N^j),
\label{eq:VBorF_PI}
\end{equation}
and evaluating the argument of the logarithm by using the recurrence relation

\begin{equation}
W_{B/F}^{(N)} = \frac{1}{N} \sum_{k=1}^N \xi^{k-1} e^{-\beta E_N^{(k)}} W_{B/F}^{(N-k)}.
\label{eq:WBorF_PI}
\end{equation}
In Eq.~\ref{eq:WBorF_PI}, $\xi=1$ for bosons, $\xi=-1$ for fermions and we set $W_{B/F}^{(0)}=1$ .
$E_N^{(k)}(R_{N-k+1},...,R_N) $ is the spring energy of k particles connected together in a long ring, given by

\begin{equation}
E_N^{(k)} = \frac{1}{2}m \omega_P^2 \sum_{l=N-k+1}^N \sum_{j=1}^P \left( {\bf r}_l^{j+1} - {\bf r}_l^{j} \right) ^2.
\label{eq:Ek}
\end{equation}
In Eq.~\ref{eq:Ek}, $r_l^{P+1}=r_{l+1}^1$ except for $l=N$, for which $r_N^{P+1}=r_{N-k+1}^1$.
We note that Eq.~\ref{eq:VBorF_PI} and~\ref{eq:WBorF_PI} lead to a slightly different expression for the potential for fermions than the one obtained by evaluating a determinant to account for particle permutations~\cite{Takahashi1984, Miura2000}. However, both methods converge to the same quantum-mechanical expectation values after integration over all particles in the partition function.
Expectation values are evaluated using the regular estimators. For a position dependent operator $\hat{O}({\bf r}_1,..,{\bf r}_N)$, such as the potential energy, the estimator $ \varepsilon_O $ is

\begin{equation}
\varepsilon_O = \frac{1}{P}\sum_{j=1}^P O({\bf r}_1^j,..,{\bf r}_N^j),
\label{eq:Est}
\end{equation}
and the expectation value is obtained by

\begin{equation}
\left\langle \hat{O} \right\rangle_I = \frac{1}{Z_I} \int \varepsilon_O e^{-\beta U^{(N)}_I} dR_1 ... dR_N \equiv \left\langle \varepsilon_O \right\rangle_I.
\label{eq:Av}
\end{equation}
For evaluating the kinetic energy we use the virial estimator~\cite{Herman1982} (see SI for more details).

The key difference between fermions and bosons is that, in the case of fermions, odd permutations carry a negative sign. Therefore, $W_F^{(N)}$ is no longer positive definite. When it becomes negative the potential $U_F^{(N)}$ is complex and cannot be sampled in standard MD or MC simulations. As mentioned in Section~\ref{sec:Intro}, using the absolute value of $W_F^{(N)}$ will result in a real potential, but with an infinite barrier when $W_F^{(N)}=0$.

Here, we propose instead to simulate the system as if it were composed of bosons, similarly to what is done in PIMC simulations~\cite{Troyer2005}.
The fermionic expectation values are then recovered from the bosonic simulations by reweighting

\begin{equation}
\left\langle \hat{O} \right\rangle_F = \frac{\left\langle \varepsilon_O s \right\rangle_B}{\left\langle s \right\rangle_B},
\label{eq:reW}
\end{equation}
where $s = W_F^{(N)}/W_B^{(N)}$ is the signed relative weight for each sampled configuration. The evaluation of $W_F^{(N)}$ is done concurrently with the evaluation of the bosonic potential, and therefore presents only a modest additional computational cost.
The average sign $ \langle s \rangle_B $ decreases exponentially with $\beta$ and the number of particles~\cite{Troyer2005}. As a result, the relative error for expectation values evaluated using Eq.~\ref{eq:reW} becomes exponentially hard to converge, which is referred to as the fermionic sign problem. In the next Section, we show that as long as  $\langle s \rangle_B$ is large enough, the simulations of electrons in two-dimensional QDs can be converged and are in very good agreement with PIMC results~\cite{Dornheim2019}. Then, we propose a procedure to alleviate the sign problem and evaluate the thermal energy of fermionic systems at lower temperatures than would otherwise have been possible using PIMD.

\section{Benchmark}
\label{sec:QDs}

To test the new method for fermionic PIMD we performed simulations of electrons in two-dimensional QDs. These materials have received much attention in recent years due to their interesting electronic, optical and catalytic properties and their potential use in technological applications~\cite{Wang2016, Xu2018, Manikandan2019}.
Landman and collaborators~\cite{Ellenberger2006, Yannouleas2007, Li2007} have shown that the two-dimensional QDs can be modelled using the dimensionless Hamiltonian

\begin{equation}
\hat{H} = -\frac{1}{2} \sum_{l=1}^N {\bf \nabla}_l^2 + \frac{1}{2}\sum_{l=1}^N {\bf r}_l^2 + \sum_{l,m>l}^N \frac{\lambda}{|{\bf r}_l - {\bf r}_m|}.
\label{eq:H_QD}
\end{equation}

In Eq.~\ref{eq:H_QD}, $ \lambda = e^2 / (\kappa l_0 \hbar \omega_0)$ is the Wigner parameter, $\kappa$ is the relative QD dielectric constant and $\omega_0$ is the frequency of the two-dimensional trap. We denote the effective mass of the electrons as $m$ and $l_0 = \sqrt{\hbar/m \omega_0}$ is the characteristic length of the dot. The Wigner parameter represents the ratio between the screened Coulomb repulsion in the QD and the confinement of the harmonic trap. When $ \lambda < 1 $ exchange effects dominate since the Coulomb repulsion is screened and, conversely, when $ \lambda > 1 $ the repulsive interaction is dominant. In the simulations below, the trap is isotropic with a frequency $\hbar \omega_0 = 5.1$ meV and the effective mass was set to $m= 0.07 m_e$ which are realistic values  for an electron in a GaAs QD~\cite{Ellenberger2006}. We use a development version of LAMMPS~\cite{Plimpton1995} to perform all simulations with a time step of 1 fs and the Nose-Hoover chains thermostat~\cite{Martyna1992}. Expectation values were converged with respect to the number of beads using $P=12$ at most.

\begin{figure}
\includegraphics[width=1.0\columnwidth]{Figure2.pdf
\caption{\label{fig:EvsN} The average thermal energy (upper panel) and sign (lower panel) as a function of the number of interacting fermions $N$ in a two-dimensional QD. The interaction strength is $\lambda=0.5$ and $\beta \hbar \omega_0=1$. Blue and orange circles represent the results obtained using PIMD for bosons and fermions, respectively. Green squares represent PIMC results of Dornheim~\cite{Dornheim2019}. Error bars are smaller than symbol size.}
\end{figure}

\begin{figure}
\includegraphics[width=1.0\columnwidth]{Figure3.pdf
\caption{\label{fig:Evsbeta} The average thermal energy (upper panel) and sign (lower panel) for $N=6$ interacting fermions ($\lambda=0.5)$ in a two-dimensional QD as a function of inverse temperature. Blue and orange circles represent the results obtained using PIMD for bosons and fermions, respectively. Green squares represent PIMC results of Dornheim~\cite{Dornheim2019}. Error bars are smaller than symbol size.}
\end{figure}

Fig.~\ref{fig:EvsN} shows the average thermal energy for a system with $\beta\hbar\omega_0=1$ and $\lambda=0.5$, as a function of system size.
Excellent agreement is obtained in comparison to PIMC, with a maximum absolute error of 0.6\% and mean absolute error of 0.4\%.
Fig.~\ref{fig:Evsbeta} and~\ref{fig:Evslambda} present the average thermal energies for $N=6$ as a function of the inverse temperature and repulsion strength. For the range of temperatures ($0.5 \le \beta \le 1$; $\lambda = 0.5$) and interaction parameters ($0 \le \lambda \le 4$; $\beta = 1$) considered here, we obtain very good agreement with PIMC results, with mean absolute errors of 0.8\% and 0.9\%, respectively. The simulations span a realistic range of interaction strength as the value of the interaction parameter in a GaAs QD is $\lambda \approx 1.55 $~\cite{Ellenberger2006}.

The lower panels of Fig.~\ref{fig:EvsN}-\ref{fig:Evslambda} also present the average sign as a function of system size, temperature and repulsion strength. They show that the average sign decreases with increasing $beta$ and number of particles, but also that the sign problem is more severe for weakly interacting than for strongly interacting electrons. This is in agreement with the detailed investigation by Dornheim~\cite{Dornheim2019} and physical intuition.
Converging the fermionic expectation values becomes harder with decreasing average sign. Of the results presented in this Section, the simulations for $N=6$, $\beta=1$ and $\lambda=0$ had the smallest average sign with $\langle s \rangle _B \approx 0.003$. They required 10 independent trajectories of $9\cdot 10 ^8$ MD steps in order to converge the energy to within 2\%. In comparison, the same simulations with $\lambda=3$ ($\langle s \rangle _B \approx 0.64$) required only 5 simulations of $75 \cdot 10 ^6$ MD steps in order to converge the energy to within 0.05\%. The error bars on expectation values were evaluated using a weighted average over the independent simulations and full details are given in the SI. The following section describes the use of the Bogoliubov free energy principle to obtain expectation values for systems with an even smaller average sign.

\begin{figure}
\includegraphics[width=1.0\columnwidth]{Figure4.pdf
\caption{\label{fig:Evslambda} The average thermal energy (upper panel) and sign (lower panel) at $\beta \hbar \omega_0=1$ for $N=6$ fermions in a two-dimensional QD as a function of interaction strength $\lambda$. Blue and orange circles represent the results obtained using PIMD for bosons and fermions, respectively. Green squares represent PIMC results of Dornheim~\cite{Dornheim2019}. Error bars are smaller than symbol size.}
\end{figure}

\section{Alleviating the sign problem}
\label{sec:sign}

Overcoming the sign problem is a formidable challenge. As mentioned above, a general solution is probably unattainable~\cite{Troyer2005}.
Nevertheless, developing methods that alleviate the sign problem for a wide class of systems and extend the boundaries of current simulations is important. Ideally, this should be done in a controlled manner.
Here, we propose a simple approach that provides accurate estimates of fermionic energies at lower temperatures. We demonstrate its usefulness for the model of electrons in two-dimensional QDs introduced in the previous Section, but the method can be more generally applied.
The key idea involves using the Bogoliubov inequality~\cite{feynman1972} to obtain an upper bound on the fermionic energies.

If the system Hamiltonian is denoted by $\hat{H}$ and the Hamiltonian of a second, auxiliary system is denoted by $\hat{H}'$, an upper bound on the difference in free energies between the two systems is given by the Bogoliubov inequality~\cite{feynman1972}

\begin{equation}
F_{\hat{H}} - F_{\hat{H}'} \le \left\langle \hat{H} - \hat{H}' \right\rangle_{\hat{H}'}.
\label{eq:Bogoliubov}
\end{equation}
In the following, we also assume that the energy of the system at low temperatures can be approximated by its free energy

\begin{equation}
\left\langle E \right\rangle_{\hat{H}} \approx \left\langle E \right\rangle_{\hat{H}'} + F_{\hat{H}} - F_{\hat{H}'}.
\label{eq:EisF}
\end{equation}
Eq.~\ref{eq:Bogoliubov} is very general and we can choose the auxiliary Hamiltonian such that it alleviates the sign problem. For example, it was shown in the previous Section that the average sign increases with repulsive interaction strength. Thus, it is possible to converge the simulations for strongly repelling fermions at temperatures lower than for weakly repelling ones. If we choose the former as our auxiliary Hamiltonian, we can obtain an upper bound on the energy of the weakly interacting system at low temperatures using the equations above. This is illustrated schematically in Fig.~\ref{fig:sign}.

\begin{figure}
\includegraphics[width=0.75\columnwidth]{Fig_Sign.jpg
\caption{\label{fig:sign} For a fixed number of particles, the average sign depends on the inverse temperature $\beta$ and the repulsion strength $\lambda$. The blue line represents some (arbitrary) critical value of the average sign. When the sign of the system is smaller (red), simulations are too expensive to converge. We propose simulating an auxiliary system that has a larger sign (green), and can be converged in practical simulations. Then, we estimate the energy of the original system, using the Bogoliubov inequality, at lower temperatures than otherwise would have been feasible using PIMD.}
\end{figure}

We demonstrate this approach for a system of three electrons confined to a two-dimensional QD~\cite{Li2007} in the limit of infinite screening ($\lambda = 0$). As was shown in section~\ref{sec:QDs}, this leads to the most severe sign problem. This is also emphasized in the upper panel of Fig.~\ref{fig:3e}. Orange circles show that converging the simulations for the non-interacting system becomes difficult at $\beta=2.5$ where the error is visibly much larger ($\sim 10\%$) than at higher temperatures.

Since it was shown by Dornheim~\cite{Dornheim2019} that short-range potentials have a larger average sign than systems with long-range interactions, we choose an auxiliary Hamiltonian in which the electrons interact with a repulsive Gaussian pair potential

\begin{equation}
V(|{\bf r}_l - {\bf r}_m|) = \frac{g}{\pi s^2}e^{-\frac{({\bf r}_l - {\bf r}_m)^2}{s^2}}.
\label{eq:int_pot}
\end{equation}
In Eq.~\ref{eq:int_pot}, $g$ and $s$ represent the interaction strength and range, respectively. In the following simulations, we used $g=16$ and $\sigma=0.5$ in harmonic oscillator units. The effective mass was set to $m=m_e$ and the frequency of the trap to $\hbar \omega_0 = 3 $ meV, as done by Runeson et al.~\cite{Runeson2018}. For each temperature, we performed 5 independent simulations of $75 \cdot 10^6$ steps each. Expectation values were converged with respect to the number of beads using $P=12$ for the non-interacting system and $P=72$ for the auxiliary system.

The bottom panel of Fig.~\ref{fig:3e} provides insight into why this approach is expected to succeed. The red symbols show the average sign of the non-interacting system as a function of temperature. It decreases sharply and is equal to $\approx 0.008$ at $\beta = 2.5$, which leads to the large error bars at this temperature in the upper panel. In contrast, the average sign for the auxiliary system decays significantly more slowly, which allows simulations at lower temperatures to be converged more easily.

The thermal energies obtained for the auxiliary system are shown in Fig.~\ref{fig:3e} (gray circles) and compared to the analytical results (green squares) for the non-interacting system. They are higher than the energies of non-interacting particles due to the added repulsion, as expected. Applying the Bogoliubov inequality (purple circles), we obtain upper bounds on the energies of the non-interacting system that agree with the analytical results within the statistical error. Most importantly, our approach allows an accurate estimate of the energy of the three-electron QD to be obtained at temperatures three times lower than would otherwise be feasible.

 The results are not very sensitive to the value of the interaction parameter, as shown in the SI, but it must be large enough to converge the simulations at lower temperatures. We note, however, that this is likely to be  dependent on the type of repulsive interaction in the auxiliary system. In this case, the energy of the repulsive system grows slowly with the interaction parameter $g$ (see SI). In other cases, one should remember that the Bogoliubov inequality provides only an upper bound. Therefore, a good strategy is to choose a repulsion large enough to converge the simulations at low temperatures but as small as possible to obtain an upper bound which is close to the real expectation value. One could also imagine choosing variationally the auxiliary potential, which is beyond the scope of this work.

\begin{figure}
\includegraphics[width=1.0\columnwidth]{Figure6.pdf
\caption{\label{fig:3e} The average thermal energy (upper panel) and sign (lower panel) for three non-interacting electrons in a two-dimensional QD as a function of inverse temperature. Orange circles represent the results obtained by converging Eq.~\ref{eq:reW} directly. Gray circles represent the results obtained for an auxiliary system and purple circles show the results obtained using the Bogoliubov inequality. Analytical results are represented by green squares. If error bars are not shown, they are smaller than symbol size. In the lower panel, red and brown diamonds present the average sign of the non-interacting system and the auxiliary system, respectively.}
\end{figure}

\section{Conclusions}
\label{sec:conclusions}

In this Communication, we present a new method for performing PIMD simulations for fermions. Since direct sampling of fermionic partition functions is not feasible in PIMD (or PIMC), we perform simulations as if the system were composed of bosons and reweight the result to obtain fermionic expectation values using Eq.~\ref{eq:reW}. We apply the new method for up to $N=7$ electrons in a two-dimensional QD and obtain excellent agreement with PIMC results. However, like PIMC and other exact methods, our approach suffers from the fermionic sign problem. We show that the average sign decreases, as expected, with increasing $\beta$ and system size but also with decreasing repulsion strength. To alleviate the sign problem for weakly interacting systems, we propose performing simulations of an auxiliary system with a larger average sign (\textit{e.g.} by adding a fictitious repulsive interaction potential) and correcting its thermal energy using the Bogoliubov inequality. The results obtained in this way provide an upper bound to the energy of the weakly interacting systems. We show that using this approach we are able to solve the problem of a three-electron QD in the limit of infinite screening, for which the sign problem is most severe. We obtain accurate energies at temperatures that are three times lower than would have been possible by trying to converge the reweighting scheme directly. Challenges still remain in order to perform such simulations for a large class of interesting systems. For example, at even lower temperatures (or for larger systems) our method too will suffer from the sign problem. However, this work extends the boundaries of PIMD simulations of fermions and we are hopeful that it will encourage development of new methods to attack this important problem.

\begin{acknowledgments}
This research was supported by the European Union Grant No. ERC-2014-ADG-670227/VARMET and the NCCR MARVEL, funded by the Swiss National Science Foundation. Calculations were carried out on the Euler cluster at ETH Zurich.
\end{acknowledgments}

\section{The virial estimator for bosons and fermions}
\label{sec:virial}

The quantum virial theorem is valid for both distinguishable and indistinguishable particles

\begin{equation}
    \langle \hat{T} \rangle_I = \frac{1}{2} \langle \sum_{l=1}^N {\bf \hat{r}}_l \cdot {\bf \hat{\nabla}}_{{\bf r}_l} V({\bf r}_1,...,{\bf r}_N) \rangle_I,
\end{equation}
where $I$ represents whether the particles are bosons (B), fermions (F) or distinguishable (D).
Therefore, the kinetic energy of bosons and fermions can be evaluated by using the estimator due to Berne et al.~\cite{Herman1982},

\begin{equation}
\varepsilon_T = \frac{1}{2P}\sum_{j=1}^P \sum_{l=1}^N {\bf r}_l^j \cdot {\bf \nabla}_{{\bf r}_l^j} V({\bf r}_1^j,...,{\bf r}_N^j).
\label{eq:Est}
\end{equation}
The only difference is that the expectation value is taken in the suitable bosonic or fermionic fictitious classical ensemble

\begin{equation}
\left\langle \hat{T} \right\rangle_I = \frac{1}{Z_I} \int \varepsilon_T e^{-\beta U^{(N)}_I} dR_1 ... dR_N \equiv \left\langle \varepsilon_T \right\rangle_I,
\label{eq:Av}
\end{equation}
where $Z_I$ and $ U^{(N)}_I$ are defined in the main text.
It is well known that this estimator is not translationally invariant but for the trapped systems considered in this paper it is not an issue. As explained in detail in the main text, Eq.~\ref{eq:Av} is used directly to evaluate the bosonic expectation values  while fermionic averages are obtained from the bosonic simulations by reweighting.

\section{Statistical error estimation}

Care must be taken when evaluating statistical errors using weighted data since different simulations may not sample equally well the reweighted ensemble of interest. For example, if one simulation mostly explored configurations which have small weights it will provide a poor estimate of the reweighted energy. This is taken into account in the error estimation by associating the result obtained from each trajectory with a weight that is equal to the sum over all instantaneous weights during the simulation.

More specifically, the results presented in the main text were computed as follows.
For each data point, we performed $M$ independent simulations of equal length. The first $10\cdot 10^6$ steps of each simulation were used for equilibration and were discarded from the statistical analysis.
Then, we evaluated the fermionic energy of simulation $j$ using Eq. 9 of the main text, denoted as $E_j$. We also associated with each simulation a weight $W_j$ defined as the sum over all instantaneous weights $s=W_F^{(N)}/W_B^{(N)}$ in that trajectory.

The reported energies are the weighted average over all independent simulations

\begin{equation}
    \bar{E}_F = \frac {\sum_{j=1}^{M} E_j W_j}{\sum_{j=1}^{M} W_j}.
\end{equation}
Then, we evaluated the effective sample size for our data,
\begin{equation}
    n = \frac{(\sum_{j=1}^M W_j)^2}{\sum_{j=1}^M W_j^2}.
\end{equation}
In our simulations, the effective sample size was close to the number of trajectories M, indicating that they were all similarly converged.
An unbiased estimate of the variance~\cite{Ambegaokar2010} is then evaluated using

\begin{equation}
    \sigma_E^2 = \frac{n}{n-1} \frac{\sum_{j=1}^{M} W_j (E_j - \bar{E}_F)^2 }{\sum_{j=1}^{M} W_j},
\end{equation}
and the statistical error associated with $\bar{E}_F$ is given by $\sigma_E/\sqrt{n}$.

We note that when $W_j=1$ the equations above reduce to the simple average of non-weighted data, which is used for evaluating the bosonic energies and the average sign $\langle s \rangle_B$. In that case, the value for each independent simulation is obtained directly from the average of the appropriate estimator without rewighting.

\section{Sensitivity to interaction strength}
We also performed simulations for a two-electron quantum dot (QD) in the infinite screening limit, using the same auxiliary Hamiltonian as in the main text, and tested the sensitivity of the results to the interaction strength parameter $g$.
The upper panel of Fig.~\ref{fig:Evsg} shows the energy of the auxiliary system as a function of $g$. It can be seen that the bosonic energies (blue) grow relatively slowly with the interaction parameter. As a result, the fermionic energies of the non-interacting system obtained from the Bogoliubov inequality are not very sensitive to the value of $g$ (purple). The lower panel shows the average sign as a function of interaction strength.

\begin{figure}
\includegraphics[width=0.5\columnwidth]{FigureS1.pdf
\caption{\label{fig:Evsg} The average thermal energy as a function of the interaction strength $g$ for two particles. The inverse temperature is $\beta \hbar \omega_0 = 6$. Blue circles represent the energies of the auxiliary bosonic system. Purple circles show the fermionic energies of the non-interacting system obtained using the Bogoliubov inequality. The black line is the analytical result. If not shown, error bars are smaller than symbol size.}
\end{figure}

redpajama_set_name: RedPajamaArXiv


text:
JPMorgan Chase & Co. Releases Report that Examines the Skills Gap in NYC
The report is part of JPMorgan Chase's $250 million initiative, New Skills at Work.
Tuesday, December 9, 2014 -
With major changes on the veterans landscape, how can philanthropy stay relevant, targeted and effective?
JPMorgan Chase & Co. Names Dalila Wilson-Scott Head of Global Philanthropy
Dalila Wilson-Scott has been named Head of Global Philanthropy for JPMorgan Chase & Co.
Goldman Sachs, JPMorgan and other PNY members highlighted in Corporate Giving Infographic
A new infographic from Double the Donation identifies the top 10 corporate givers for 2013, and among them are PNY members Goldman Sachs, JPMorgan Chase, Bank of America and Target.
New Banking Services Aimed At Low-Income Customers
To serve the needs of low-income customers, Bank of America and JPMorgan Chase are among U.S. financial institutions introducing new products, and to expose the high costs of living without a bank account, American Express has sponsored a 40-minute...
In A Shift In Giving, JPMorgan Chase Focusing On Economic Growth
A major shift is taking place at the JPMorgan Chase Foundation as it moves away from "broad-based giving" to a focus on "economic growth," according to Bruce McNamer, chief executive.
Bloggers Falsely Accuse JPMorgan Chase of Employee "LGBT Loyalty Test"
JPMorgan Chase appears to be the victim of right wing bloggers who have been making erroneous posts alleging the bank requires its employees to take an "LGBT loyalty" test.
JPMorgan Expands 'The Fellowship Initiative' To Help Disadvantaged High Schoolers Get Into Top Colleges
Launched four year's ago in NYC to help disadvantaged high school students get into top colleges, JPMorgan Chase's "The Fellowship Initiative" is expanding to Chicago and Los Angeles.
Why Do Banks Care About Youth Career Readiness in New York?
JP Morgan Chase recently announced a $250 million initiative to bolster the skills of workers, with a big focus on young people and three months later, the Citi Foundation also announced its biggest initiative ever: a $50 million, three-year effort...
JPMorgan to Commit $100-Million to Boost Detroit's Recovery
Wall Street giant JPMorgan Chase will commit $100-million in grants and loans over five years to aid Detroit's revitalization effort as the city recovers from the country's largest municipal bankruptcy, The New York Times and the Detroit Free Press...
8 Characteristics of Successful Venture Philanthropies
The Rockefeller Foundation hosted the Organization for Economic Cooperation and Development (OECD) for the launch of a new study on venture philanthropy.
United Way of New York City Appoints Michael Carren as New Chief Strategy and Operating Officer
United Way of New York City has announced the appointment of Michael Carren, former Director of Global Employee Engagement and Volunteerism at JPMorgan Chase, to the role of Chief Strategy and Operating Officer.
United Way of New York City
Philanthropic Advisors Network - Pilot Meeting
Thursday, October 24, 2013 -
Philanthropic advisors and consultants have been longstanding members and contributors to the Philanthropy New York community. Based on feedback from members, Philanthropy New York is piloting a peer network for philanthropic advisors to build...
Like Peanut Butter and Chocolate: Nonprofit and Community College Workforce Development Partnerships
Thursday, December 8, 2011 -
The workforce development climate is increasingly difficult. Public and private funding is shrinking meanwhile there is a greater need for programs and services as unemployed, disadvantaged, and incumbent workers with outdated skills are becoming...
The New Rapid Deployment: Resources for Returning Veterans
Monday, December 3, 2012 - 4:30pm to Tuesday, December 4, 2012 - 3:00pm
Thousands of Iraq and Afghanistan veterans are returning home to New York City. Though few funders consider veterans' issues to be a direct part of their mission, many of our members still want to support these returning New Yorkers. We invite you...

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text:
Top Paying Jobs With a Kinesiology Degree
by Jayne Thompson; Updated June 29, 2018
1 Jobs for Health & Human Kinetics Majors
2 For How Long Do You Go to College to Be a Physical Therapist and What Is the Average Income?
3 Train to Be Children's Fitness Instructor
4 Qualifications of a Kinesiologist
If you've chosen to major in kinesiology, you likely have a fascination with sports, physical performance and the movement of the human body. Obvious career choices include fitness training, dance instruction and sports coaching, but you have several other options if you want a well-paying career.
Physical therapists use their kinesiology training to help people recover from physical injuries, improve their movement and manage pain. The work is varied, with duties ranging from rehabilitating stroke patients who have lost mobility to helping someone recover from a sports injury. As of 2017, the median annual wage for physical therapists was $86,850, and the top 10 percent tier earned more than $122,650. A degree in kinesiology is a good entry point for this career. However, you will have to take an additional three-year program offering a Doctor of Physical Therapy degree.
Similar to physical therapists, occupational therapists use hands-on techniques to rehabilitate patients with disabilities and chronic injuries. Here, the focus is helping patients regain the skills they need for everyday living, for example, teaching newly disabled patients to cook, get dressed and use adaptive equipment such as leg braces and mobility aids. The median annual occupational therapy pay was $83,200 in 2017, rising to $120,440 for the best-paid 10 percent. Additional training is necessary – you'll need to hold at least a master's degree to gain state licensure as an occupational therapist. Programs usually take two or three years to complete.
Outside of healthcare, your kinesiology education should translate well to a career as a high school physical education teacher. The median annual wage here comes in at $59,170, rising to $95,380 for the top 10 percent. You'll need to complete a teacher preparation program and have supervised experience in teaching, which you'll typically gain in the classroom and on the sports field. Perks include a paid two-month break during the summer and plenty of opportunities to teach summer-school programs.
An interest in sports and physical activity could segue nicely to a career in sports marketing, a niche area within the marketing field. Sports marketing associates work to promote teams, players and sporting events and stir up the public's enthusiasm so they want to buy merchandise or a ticket to watch the athletes play. While there's no specific entry requirement to this profession, you'll generally need marketing knowledge alongside your specialized kinesiology education. Some employers will encourage you to go back to school and obtain a Master of Business Administration that may carry the specialty of sports marketing. It's well worth going back to school for an extra year or two. The Bureau of Labor Statistics suggests that median pay for marketing managers is $132,230 per year, and there may be more cash in the pot, depending on the popularity of the sport you are promoting.
American Kinesiology Association: Careers in Kinesiology
Bureau of Labor Statistics: Physical Therapy
Bureau of Labor Statistics: Occupational Therapy
Bureau of Labor Statistics: High School Teacher
Bureau of Labor Statistics: Advertising, Promotions and Marketing Managers
American Kinesiology Association: About Us
Jayne Thompson earned an LLB in Law and Business Administration from the University of Birmingham and an LLM in International Law from the University of East London. She practiced in various "big law" firms before launching a career as a business writer. Her articles have appeared on numerous business sites including Typefinder, Women in Business, Startwire and Indeed.com. Find her at www.whiterosecopywriting.com.
Thompson, Jayne. "Top Paying Jobs With a Kinesiology Degree." Work - Chron.com, http://work.chron.com/top-paying-jobs-kinesiology-degree-17777.html. 29 June 2018.
Thompson, Jayne. (2018, June 29). Top Paying Jobs With a Kinesiology Degree. Work - Chron.com. Retrieved from http://work.chron.com/top-paying-jobs-kinesiology-degree-17777.html
Thompson, Jayne. "Top Paying Jobs With a Kinesiology Degree" last modified June 29, 2018. http://work.chron.com/top-paying-jobs-kinesiology-degree-17777.html
What Degree Do You Need to Be a Gym Teacher?
Careers With a Master's Degree in Exercise Science
Does an Exercise Science Major Apply to Physical Therapy?
What Kind of Schooling Should I Take to Become a Gym Teacher?
Top Paid Careers for Kinesiology Majors
Pay Scale for an Athletic Trainer Master
Classes to Become a Gym Teacher
What Kind of Jobs Can You Get With a Sports Science Major?
Pediatric Physical Therapy Activities
The Difference Between an Athletic Trainer & a Physical Therapist
Become a Massage Therapist Going to a Real College


It has come to our attention that the name Bates Wells & Braithwaite London LLP is being used to request sums of money to be deposited into an unknown bank account through the use of fraudulent invoices containing our firm's name and logo.
A member of the public was contacted by an individual, calling himself 'David Campbell', who purported to be working with this firm. The email address used by this individual was campbelldavid205@gmail.com. The invoice contains a phone number, 0303 123 1111, and an email address, k.lowe@bwbwllp.com. This phone number and email address do not belong to any member of Bates Wells staff and should not be responded to.
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Why Obama might veto defense bill: It would hurt the fight against terrorism
Analysis: Inside the administration's thinking on terrorism detentions.
Marc Ambinder
Whatever President Obama's legacy may be, he does not want to be seen as the commander in chief who turned the United States into the world's jailer of Muslims without charge. But it's not because he's soft on terrorism. Two administration officials confirmed Friday that the president isn't bluffing about his threat to veto the defense authorization bill if its new detainee provisions aren't substantially modified. That puts the president in the unusual position of wielding the veto pen against a political ally, Senate Armed Services Committee Chairman Carl Levin, D-Mich., who along with some strange Republican bedfellows, is pushing to beef up the military's role in handling suspected terrorists. In the Senate, debate has focused largely on whether American citizens would be subject to the proposed new law's sweeping powers. In legal circles, it's about the wisdom and morality of further codifying a system of indefinite attention. But for the Obama administration, it's also about the future of counterterrorism. The theory behind the Senate's approach is this: the legislation basically creates a large broom that sweeps a large category of terrorists who might be covered under the Authorization for the Use of Military Force against the Taliban and al-Qaida into the military detention system on the assumption that they are combatants in a war, that the battlefield extends to the U.S., and that the military knows how to deal with combatants better than federal agents. Then there's intelligence. As Sen. Lindsey Graham, R-S.C., an architect of the detainee provisions has said, "if you take the ability to hold someone as an enemy combatant off the table, you cannot interrogate them for intelligence-gathering purposes, and if you put a time limit on how long you can hold them, you defeat the purpose of gathering intelligence." The administration foresees a potential catastrophe. This rigid approach could impede intelligence collection, and even result in dangerous people being set free. For one thing, every detainee picked up and held by the U.S. outside the warzones like Iraq and Afghanistan can seek a habeas corpus hearing in front of a federal judge, requiring the administration to prove the association between the combatant and al-Qaida, or the Taliban, or associated forces, in order to keep them in military detention. Often, the government will be disinclined to lay out the proof-possibly because it doesn't exist or because the providing the proof could compromise sensitive sources or methods, a sophisticated technical intelligence platform, or a liaison intelligence service. "Detention issues are much more complex than most people realize," Nathaniel P. Jones, a director for counter-terrorism on the National Security Council, said in an interview. "The only responsible way to handle these issues is to let the unique facts and circumstances of each case, and the advice of experienced professionals who have access to those facts, drive our decisions about which set of authorities to use to detain and try suspected terrorists." With "a rigid, ideological, one-size-fits-all approach like the one being advocated in Congress, intelligence will be lost and dangerous individuals will be set free," he said. Letters to Congress from the directors of the FBI and CIA, as well as the National Intelligence Director James Clapper buttress this contention. Practically, the administration argues that following this approach, the U.S. can avoid having to hold people without charges, and it doesn't compromise our intelligence collection. Despite what the Senate says, trying to paper this over with waivers and additional bureaucracy will not solve the fundamental problems with an approach that mandates military custody…which it hasn't really explained - beyond calling terrorism "war" - why such an approach is needed. One provision of the bill would require that many terrorists associated with al-Qaida, no matter where they are apprehended, be turned over to the military. The House version of the bill would require terrorist suspects to appear before a military commission or be held indefinitely. An amendment suggests that U.S. citizens are not automatically covered by the provision. That of course, means they are not automatically not covered either. Some of the bill's sponsors have said the presumption of association with al-Qaida would mean that anyone who is picked up in the U.S. on a terrorism-related charge and who appears to have some connection to al-Qaida --- maybe a website they browsed - could be denied access to an attorney and subject to immediate transfer to the custody of the U.S. military. There's a waiver process, which Congress added to provide a fig leaf of flexibility. The Secretary of Defense can certify to Congress that a federal trial would be better. But the procedures here are unclear and likely to run headlong into legal challenges. The FBI can't detain categories of terrorists without the waiver saying they can, which is illogical. The FBI cannot interrogate someone without someone getting permission from Secretary of Defense, presenting to him with the details of the case, and submitting his affirmation to Congress. "The legislation as currently drafted will inhibit our ability to convince covered arrestees to cooperate immediately, and provide critical intelligence," writes FBI director Robert Mueller in his letter to Congress. The ad hoc system in place now, as messy as it is, gives the executive branch more flexibility, giving U.S. officials the ability to hold a suspect until they figure out how they want to proceed. It's imperfect and raises all sorts of tough questions, but it does not require a rush to judgment and does permit a careful collection and examination of the evidence. Ahmed Abdulkadir Warsame, a Somali, was held by the administration for two months on a U.S. Navy vessel while the government decided how to charge him. Because federal courts jurisdiction is much broader and the list of offenses for which a suspect can be charged much longer, counterterrorism professionals determined the safer route - both for purposes of protecting classified information and ensuring the right outcome - was to charge and try him in civil courts. To establish jurisdiction in a military commission or hold him in military detention, the government would have to not only link him to al-Shabaab and al-Qaida in the Arabian Peninsula, but also demonstrate - with sufficient evidence - that Warsame was part of al-Qaida. Because that is not required in federal court, his prosecution there posed less of a litigation risk, and would not require the use of more sensitive intelligence. Warsame will get a presumption of innocence vindicated, but if the goal here, even for hawks, is to get bad guys out of the battlefield, and permanently, the federal trial is a safer bet. An American jury might acquit a terrorism suspect, but the after Congressional reforms to the military commission system, there's no reason to think that's any more likely to happen in federal courts than in a military commission. To the consternation of many, the Obama administration reserves the right to hold suspected terrorists pursuant to the AUMF where it is appropriate to do so, as it did with Warsame. But to do so, it has to defend that detention in court, which is not always possible. It could put the government in a position of having to lay out that classified evidence that wouldn't be required in a civilian prosecution. Wouldn't the administration have to prove a linkage in federal court? Not at all. Federal officials can charge the person with materially supporting any designated terrorist group, regardless of the individual's or group's connections to al-Qaida. They can simply use the offense itself, something that they cannot do for military commissions, which, by their definition, can only be used to try members of al-Qaida or others we can demonstrate are involved in an armed conflict with the United States. Example: the FBI's ace counter-terrorism team in Seattle arrested two Americans, Khalid Abdul-Latif and Walli Mujahidh in June for conspiring to attack a military recruiting center. The government may - or may not - have evidence linking them to al-Qaida. If the feds do, maybe the evidence was provided to them by a country that doesn't want its cooperation known. It didn't matter: The two were held on charges that will send them to prison for 50 years if they are found guilty. If the Senate bill is signed into law, some argue these two men would be in military custody… or maybe even free, if the government can't, or won't, prove their links to al-Qaida. (To be fair, it's not clear from the text whether "home grown" extremists would actually be covered by the Senate legislation, but the intent of those who wrote it suggests that the answer is yes, even though the administration might disagree.) An irony here is that the Senate bill, while seeming to get tough on terrorists,will make it harder to bring certain of them to justice. Or maybe it's not an irony: the net effect of this bill, were Obama to sign it, would be the creation of a significant disincentive to capture terrorists or facilitators who might possess intelligence about future attacks. Instead, there would be a larger incentive to simply kill them. Congress seems to think that the AUMF detainees are all snatchable or killable by U.S. special operations forces. That's not true. Many are rounded up in countries with which the U.S. is not at war. And whatever fantasies you harbor about the Joint Special Operations Command operating in a European capital, no Delta Force element is going to grab someone in Berlin anytime soon. No problem, if the country would turn over the person to the U.S. But the proposed Senate legislation makes that less likely. In classified briefings, the administration has presented to Congress examples of people who are in custody overseas and who would be transferred to the U.S. were it not for the likelihood that they'd end up in the military commission or detention system. It's not just Western Europe: countries around the world - from the Middle East to Southeast Asia - are unlikely to turn over Muslims to the U.S. military to be held in indefinite detention or tried in a military commission for reasons that should that should be manifest. On intelligence, most counter-terrorism experts seem to think that the procedures in place for gathering time-sensitive information are sufficient, and that the Miranda process, which applies to terrorists arrested by the FBI, doesn't hinder that urgent national security need. The leverage of the military system, ostensibly in the fear that it would create in detainees or in the expertise of military interrogators, is weighed against the leverage that federal prosecutors have - and, of course, the track record of FBI interrogators (or interrogators who are part of the newly-formed High Value Interrogation Group team). David Headley was handled through the criminal justice system, provided valuable intelligence, and was ultimately sentenced to life in prison for his role in the Mumbai massacre in 2000. Headley is one example in a long list of intelligence successes in our federal courts. A deal might have been possible early on, when the Armed Services Committee was drafting the bill. Levin might have subtracted some of the provisions he secretly negotiated in exchange for codifying military detention of al-Qaida suspects picked up overseas, or perhaps the near-term eschewing of a new prison for detainees inside the United States. Many Democrats were surprised when Levin unveiled his language on detention. But they need not be. He does not want to be the first Armed Services Committee chair in decades to fail to produce a defense policy bill. And in these poisonously partisan times, a compromise on detainees is the only way he's going to get votes. The theory behind the Senate's approach is this: the legislation basically creates a large broom that sweeps a large category of terrorists who might be covered under the Authorization for the Use of Military Force against the Taliban and Al Qaeda into the military detention system on the assumption that they are combatants in a war, that the battlefield extends to the U.S., and that the military knows how to deal with combatants better than federal agents. Then there's intelligence. As Lindsey Graham, an architect of the detainee provisions has said, if you take the ability to hold someone as an enemy combatant off the table, you cannot interrogate them for intelligence-gathering purposes, and if you put a time limit on how long you can hold them, you defeat the purpose of gathering intelligence." The administration foresees a potential catastrophe. This rigid approach could impede intelligence collection, and even result in dangerous people being set free. For one thing, every detainee picked up and held by the U.S. outside the warzones like Iraq and Afghanistan can seek a habeas corpus hearing in front of a federal judge, during which the administration will have to prove the association between the combatant and Al Qaeda, or the Taliban, or associated forces. Often, the government will be disinclined to lay out the proof. For one thing, they might not have proof. Or, the proof comes from a very sensitive source or method: an agent, a sophisticated technical intelligence platform, or a liaison intelligence service.
NEXT STORY: Clinton moves to inject new urgency into bioweapon concerns at Geneva event


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Swecha will be conducting a Workshop at the VR Siddhartha Engineering College on 24th and 25th of August. The Workshop shall focus on Free Software philosophy, Python and Software Testing Methodology & Automation Tools.
Swecha organized One-day workshop in Malla Laxma Reddy Institute of Technology & Management on 30th June, 2012..


One day I really hope a book is written about the making of Mighty No. 9 because I bet there is quite the story to tell here. Most people reading this I'm sure are familiar with the game's history. The game was launched on Kickstarter in August 2013, and went on to raise almost four million dollars. The Kickstarter campaign came at the perfect time, when legions of Mega Man fans were not happy with the way Capcom was treating the franchise. The idea of a spiritual successor was appealing, to myself as well. I didn't end up putting any money towards funding the game, but I do remember considering it.
From there, it was as though they made a list of all the worst decisions to make following a successful Kickstarter campaign and proceeded to tick off each item one by one. The game was delayed repeatedly, a separate Kickstarter was run for a different game while this one was still in the midst of a troubled production, there was hostility with the appointed community manager, and the list goes on. Then when the game finally saw the light of day, backers were not given their codes in a timely manner and many that did received ones for the wrong platform or one that flat-out didn't work. The last I saw, not a single person had received any of their physical rewards either, and my understanding is that Comcept (the company behind the game) has been radio silent on the matter. They did speak up long enough for a developer to state that the game isn't perfect, but is better than nothing. Add poor reviews on top of all that and you have yourself a Kickstarter debacle.
I admit, the only reason I own a physical copy of Mighty No. 9 is because I pre-ordered it over a year ago and completely forgot about it until I got a shipping notice email letting me know that it was on its way. The price was low and I was curious, so I was not too upset about the surprise. I have now played Mighty No 9 and I can say I feel the terms "disaster" and "trainwreck", both of which I have seen used on numerous occasions, are an exaggeration (at least for the game itself). Terms like "bland" and "crushingly mediocre" are definitely much more apt.
Mighty No 9 has a story. It is not interesting in the slightest. A scientist created a bunch of robots, each labeled as Mighty No 1-8, and now they are all evil. No 9 has to go through eight stages, in the order the player chooses, and snap each robot out of it and get their power, which can then be used to defeat the other robots. There are cut scenes between each stage and they, wow they do not look good. Everything looks so dull and basic, and the characters don't even move their mouths when they speak so they all look like slack jawed crazy people. If I'm not mistaken, after the initial Kickstarter, additional funds were sought in order to provide full English voice acting and what we end up with is wooden and consistently poor. It's hard enough to care about the story as is, but when the voices trying to sell it to you are this dull, the whole narrative doesn't stand a chance.
The presentation issues aren't limited to the cut scenes. The art style of this game is just so…blah. I wonder if it has to do with needing the game to run on nearly every video game platform that currently exists, but everything about this is flat and well, boring. I typically don't like to make statements like this, but this game truly looks like something you would have seen in the initial stages of Xbox Live Arcade. From Beck's (that's the main character's actual name) running animation that doesn't seem to match his actual speed, to the uninspired character design, to the downright laughable explosion effects (which are used very frequently) there is almost nothing visually appealing here.
In terms of the actual game, it does NOT make a good first impression. I was ready to stop playing right after the first stage. The movement felt slow, the shooting felt bad, enemies were taking way too long to kill and the stage design was bland. I persevered though and once I started to get a better hang on the game's poorly explained mechanics, I started to appreciate it far more.
The main mechanic here is the dash move, which not only factors into your traversal (moving forward faster and its often necessary to navigate the environment), but into the combat as well. Once an enemy has been shot a number of times, their colour changes and they become dizzy, allowing you to dash through them. This kills them instantly and allows you to absorb their power, which can increase your firepower, speed, etc. I have to say, when you get a good dash run going, it can feel quite good. It's satisfying to zip your way through a series of enemies, becoming more powerful all the while. The problem is that the stages often didn't lend themselves well to getting a good chain going, often quickly putting you back in the situation of having to deal with its typically sluggish pace.
The stage select portion of Mega Man is of course one of the most notable elements of the series. Each robot master would grant you a different power and each robot master had a weakness to one of those powers. Finding what ability works best with which boss was always one of my favourite parts of those games. Mighty No 9 attempts that. It has eight stages with eight bosses. Each gives you a power that hypothetically works best against another boss. The problem is, I never really needed to exploit those weaknesses. I employed a similar strategy here that I do with the Mega Man games in that my first go at the boss is always done with the regular weapon as I get a sense of his pattern. When I did that here, almost every time I realized that the regular weapon worked just fine against the boss, sometimes even beating them on the first go. So I never really had to experiment with any of the weapons. Yes, that's on me as I easily could have done so, but the game never made it seem necessary so I mean, why bother? In fact, the powers as a whole never seemed necessary until one of the last stages, which makes effective use of them. You have to utilize different powers to progress through the level, and it was the only real time it felt like my various abilities were being put to good use. The one nice touch is that if you are in a stage and possess the weapon the boss is vulnerable to, the boss that weapon previously belonged to will show up at some point during the stage and effect it in some way. The stages don't change in a strong meaningful way, but at the very least it's a nice, added touch.
That ties into a bigger issue – the stage design. The original Mega Man games had consistently memorable levels. Each one felt unique, tied to its particular robot master in a meaningful way that gave the whole thing a large amount of personality. There are moments and encounters in those games that I remember to this day. Mighty No 9 has none of that. The stages are fine, with a couple that do stand-out. The highlight for me was the Capitol Building stage, whose boss, Countershade, spends the level trying to snipe you down. This requires you to dodge his distant fire as you make your way through the stage. It was one of the last stages I played and was the rare one that had a gimmick to it, something that made it stand out from the others. Most of the other levels feel cobbled together at random, like somebody made them in a Mega Man level editor.
Outside of the main story, there's also a Challenge Mode which, though I haven't completed all of the stages, does seem to make decent use of your various powers. Though a run of the early challenges simply has you play through the exact same "Destroy all the Targets" level, but with each individual power. So it's a mixed bag, but at least it's there if you want more Mighty No. 9. There's also a boss rush mode, if you want to play through a run of forgetful boss fights one after another.
That's a lot of negatives so let me say that I don't think all of that adds up to make a terrible game. It's fine, its just so thoroughly fine that I can't muster up any enthusiasm for it. I can't say you should play it, but I also can't say that you shouldn't. I finished the main story in about 4 hours, didn't strongly dislike the time I spent with it but also was not unhappy that the credits (which are almost the length of the game itself due to all the Kickstarter backers listed) were rolling. It's a perfectly fine game that, if it didn't have the history it does, would likely fade away into obscurity amongst so many other unremarkable digital titles.


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