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The use of generative AI-based coding assistants like ChatGPT and Github Copilot is a reality in contemporary software development. Many of these tools are provided as remote APIs. Using third-party APIs raises data privacy and security concerns for client companies, which motivates the use of locally-deployed language models. In this study, we explore the trade-off between model accuracy and energy consumption, aiming to provide valuable insights to help developers make informed decisions when selecting a language model. We investigate the performance of 18 families of LLMs in typical software development tasks on two real-world infrastructures, a commodity GPU and a powerful AI-specific GPU. Given that deploying LLMs locally requires powerful infrastructure which might not be affordable for everyone, we consider both full-precision and quantized models. Our findings reveal that employing a big LLM with a higher energy budget does not always translate to significantly improved accuracy. Additionally, quantized versions of large models generally offer better efficiency and accuracy compared to full-precision versions of medium-sized ones. Apart from that, not a single model is suitable for all types of software development tasks.

We propose a number of concepts and properties related to `weighted' statistical inference where the observed data are classified in accordance with a `value' of a sample string. The motivation comes from the concepts of weighted information and weighted entropy that proved useful in industrial/microeconomic and medical statistics. We focus on applications relevant in hypothesis testing and an analysis of exponential families. Several notions, bounds and asymptotics are established, which generalize their counterparts well-known in standard statistical research. It includes Stein-Sanov theorem, Pinsker's, Bretangnole-Huber and van Trees inequalities and Kullback--Leibler, Bhattacharya, Bregman, Burbea-Rao, Chernoff, Renyi and Tsallis divergences., Comment: 42 pages

We study the problem of optimal risk policies and dividend strategies for an insurance company operating under the constraint that the timing of shareholder payouts is governed by the arrival times of a Poisson process. Concurrently, risk control is continuously managed through proportional reinsurance. Our analysis confirms the optimality of a periodic-classical barrier strategy for maximizing the expected net present value until the first instance of bankruptcy across all admissible periodic-classical strategies.

Generating context specific data quality deficits is necessary to experimentally assess data quality of data-driven (artificial intelligence (AI) or machine learning (ML)) applications. In this paper we present badgers, an extensible open-source Python library to generate data quality deficits (outliers, imbalanced data, drift, etc.) for different modalities (tabular data, time-series, text, etc.). The documentation is accessible at https://fraunhofer-iese.github.io/badgers/ and the source code at https://github.com/Fraunhofer-IESE/badgers, Comment: 17 pages, 16 figures

In this paper, we study the regularity of the value function associated with a stochastic control problem where two controls act simultaneously on a modulated multidimensional diffusion process. The first is a switching control modelling a random clock. Every time the random clock rings, the generator matrix is replaced by another, resulting in a different dynamic for the finite state Markov chain of the modulated diffusion process. The second is a singular stochastic control that is executed on the process within each regime., Comment: arXiv admin note: substantial text overlap with arXiv:2006.13595

Magnetotellurics (MT) is a passive electromagnetic geophysical method that measures variations in subsurface electrical resistivity. MT data are collected in the time domain and processed in the frequency domain to produce estimates of a transfer function representing the Earth's electrical structure. Unfortunately, the MT community lacks metadata and data standards for time series data. As the community grows and findability, accessibility, interoperability, and reuse of digital assets (FAIR) data principles are enforced by government and funding agencies, a standard is needed for time series data. Presented here is a hierarchical data format (MTH5) that is logically formatted to how MT data are collected. Open-source Python packages are also described to read, write, and manipulate MTH5 files. These include a package to deal with metadata (\texttt{mt\symbol{95}metadata}) based on standards developed by the Working Group for Magnetotelluric Data Handling and Software assembled by the Incorporated Research Institutions for Seismology (IRIS), and \texttt{mth5}: a package to interact with MTH5 files that uses \texttt{mt\symbol{95}metadata}. Example code and workflows are presented.

This paper studies {a} mixed singular/switching stochastic control problem for a multidimensional diffusion with multiples regimes on a bounded domain. Using probabilistic, partial differential equation (PDE) and penalization techniques, we show that the value function associated with this problem agrees with the solution to a Hamilton-Jacobi-Bellman (HJB) equation. In that way, we see that the regularity of the value function is $C^{0,1}\cap\W^{2,\infty}_{loc}$.

In this paper we aim to study an optimal insurance premium level for health-care in a deterministic and stochastic SIR models with migration fluxes and vaccination of population. The studied model considers two standard SIR centres connected via links and continuous migration fluxes. The premium is calculated using the basic equivalence principle. Even in this simple setup there are non-intuitive results that illustrate how the premium depends on migration rates, severeness of a disease and initial distribution of healthy and infected individuals through the centres. We investigate how the vaccination program effects the insurance costs by comparing the savings in benefits with the expenses for vaccination. We compare the results of deterministic and stochastic models.

This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching Markov chain. For this model, we 1) give finite sample bounds on the occupancy probabilities, and 2) provide detailed asymptotics in the case where the underlying distribution is regularly varying. We find that, in the regularly varying case, the finite sample bounds are rate optimal and have, up to a constant, the same rate of decay as the asymptotic result.

The aim of this work is to investigate the optimal vaccine sharing between two SIR centers in the presence of migration fluxes of susceptibles and infected individuals during the mumps outbreak. Optimality of the vaccine allocation means the minimization of the total number of lost working days during the whole period of epidemic outbreak $[0,t_f]$, which can be described by the functional $Q=\int_0^{t_f}I(t){\rm d}t$ where $I(t)$ stands for the number of infectives at time $t$. We explain the behavior of the optimal allocation, which depends on the model parameters and the amount of available vaccine.

We present the SecureCloud EU Horizon 2020 project, whose goal is to enable new big data applications that use sensitive data in the cloud without compromising data security and privacy. For this, SecureCloud designs and develops a layered architecture that allows for (i) the secure creation and deployment of secure micro-services; (ii) the secure integration of individual micro-services to full-fledged big data applications; and (iii) the secure execution of these applications within untrusted cloud environments. To provide security guarantees, SecureCloud leverages novel security mechanisms present in recent commodity CPUs, in particular, Intel's Software Guard Extensions (SGX). SecureCloud applies this architecture to big data applications in the context of smart grids. We describe the SecureCloud approach, initial results, and considered use cases., Comment: 4 pages. Lausanne, Switzerland

This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of the Fisher information inequality and entropy power inequality for the weighted entropy and discuss connections with weighted Lieb's splitting inequality. The concepts of rates of the weighted entropy and information are also discussed., Comment: Published at http://dx.doi.org/10.15559/17-VMSTA85 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)

Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, the logarithmic growth rate leads to a supermartingale, and (B) the optimal (martingale) investment strategy is a proportional betting. We focus on properties of the optimal portfolios and discuss a number of simple examples extending the well-known Kelly betting scheme. An important restriction is that the investment does not exceed the current capital value and allows the trader to cover the worst possible losses. The paper deals with a class of discrete-time models. A continuous-time extension is a topic of an ongoing study.

Blockchains such as Bitcoin and Ethereum execute payment transactions securely, but their performance is limited by the need for global consensus. Payment networks overcome this limitation through off-chain transactions. Instead of writing to the blockchain for each transaction, they only settle the final payment balances with the underlying blockchain. When executing off-chain transactions in current payment networks, parties must access the blockchain within bounded time to detect misbehaving parties that deviate from the protocol. This opens a window for attacks in which a malicious party can steal funds by deliberately delaying other parties' blockchain access and prevents parties from using payment networks when disconnected from the blockchain. We present Teechain, the first layer-two payment network that executes off-chain transactions asynchronously with respect to the underlying blockchain. To prevent parties from misbehaving, Teechain uses treasuries, protected by hardware trusted execution environments (TEEs), to establish off-chain payment channels between parties. Treasuries maintain collateral funds and can exchange transactions efficiently and securely, without interacting with the underlying blockchain. To mitigate against treasury failures and to avoid having to trust all TEEs, Teechain replicates the state of treasuries using committee chains, a new variant of chain replication with threshold secret sharing. Teechain achieves at least a 33x higher transaction throughput than the state-of-the-art Lightning payment network. A 30-machine Teechain deployment can handle over 1 million Bitcoin transactions per second.

A random flight on a plane with non-isotropic displacements at the moments of direction changes is considered. In the case of exponentially distributed flight lengths a Gaussian limit theorem is proved for the position of a particle in the scheme of series when jump lengths and non-isotropic displacements tend to zero. If the flight lengths have a folded Cauchy distribution the limiting distribution of the particle position is a convolution of the circular bivariate Cauchy distribution with a Gaussian law., Comment: Published at http://dx.doi.org/10.15559/17-VMSTA75 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)

In this paper, we guarantee the existence and uniqueness (in the almost everywhere sense) of the solution to a Hamilton-Jacobi-Bellman (HJB) equation with gradient constraint and a partial integro-differential operator whose L\'evy measure has bounded variation. This type of equation arises in a singular control problem, where the state process is a multidimensional jump-diffusion with jumps of finite variation and infinite activity. We verify, by means of {\epsilon}-penalized controls, that the value function associated with this problem satisfies the aforementioned HJB equation.

Accountability aims to provide explanations for why unwanted situations occurred, thus providing means to assign responsibility and liability. As such, accountability has slightly different meanings across the sciences. In computer science, our focus is on providing explanations for technical systems, in particular if they interact with their physical environment using sensors and actuators and may do serious harm. Accountability is relevant when considering safety, security and privacy properties and we realize that all these incarnations are facets of the same core idea. Hence, in this paper we motivate and propose a model for accountability infrastructures that is expressive enough to capture all of these domains. At its core, this model leverages formal causality models from the literature in order to provide a solid reasoning framework. We show how this model can be instantiated for several real-world use cases., Comment: In Proceedings CREST 2016, arXiv:1608.07398

In this paper, we review Fisher information matrices properties in weighted version and discuss inequalities/bounds on it by using reduced weight functions. In particular, an extended form of the Fisher information inequality previously established in [6] is given. Further, along with generalized De-Bruijn's identity, we provide new interpretation of the concavity for the entropy power., Comment: The paper is wihdrawn as it needs improvement

The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. In this paper, we establish a number of simple inequalities for the weighted entropies (general as well as specific), mirroring similar bounds on standard (Shannon) entropies and related quantities. The required assumptions are written in terms of various expectations of the weight functions. Examples are weighted Ky Fan and weighted Hadamard inequalities involving determinants of positive-definite matrices, and weighted Cram\'{e}r-Rao inequalities involving the weighted Fisher information matrix., Comment: arXiv admin note: substantial text overlap with arXiv:1409.4102

We provide sharp error bounds for the difference between the transition densities of some multidimensional Continuous Time Markov Chains (CTMC) and the fundamental solutions of some fractional in time Partial (Integro) Differential Equations (P(I)DEs). Namely, we consider equations involving a time fractional derivative of Caputo type and a spatial operator corresponding to the generator of a non degenerate Brownian or stable driven Stochastic Differential Equation (SDE)., Comment: 36 pages

Following the paper by Algoet--Cover (1988), we analyse log-optimal portfolios where return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, logarithmic growth rate is a supermartingale, and (B) the optimal (martingale) investment strategy is a proportional betting; it does not depend on the form of the weight function, although the optimal rate does. The existence of an optimal investment strategy has been established earlier in a great generality by Kramkov--Schachermayer (2003) although our underlying assumptions are different.

Epidemic dynamics in a stochastic network of interacting epidemic centers is considered. The epidemic and migration processes are modelled by Markov's chains. Explicit formulas for probability distribution of the migration process are derived. Dependence of outbreak parameters on initial parameters, population, coupling parameters is examined analytically and numerically. The mean field approximation for a general migration process is derived. An approximate method allowing computation of statistical moments for networks with highly populated centres is proposed and tested numerically., Comment: 27 pages, 10 figures (17 plots)

We consider a Bayesian problem of estimating of probability of success in a series of conditionally independent trials with binary outcomes. We study the asymptotic behaviour of differential entropy for posterior probability density function conditional on $x$ successes after $n$ conditionally independent trials, when $n \to \infty$. It is shown that after an appropriate normalization in cases $x \sim n$ and $x$ $\sim n^\beta$ ($0<\beta<1$) limiting distribution is Gaussian and the differential entropy of standardized RV converges to differential entropy of standard Gaussian random variable. When $x$ or $n-x$ is a constant the limiting distribution in not Gaussian, but still the asymptotic of differential entropy can be found explicitly. Then suppose that one is interested to know whether the coin is fair or not and for large $n$ is interested in the true frequency. To do so the concept of weighted differential entropy introduced in \cite{Belis1968} is used when the frequency $\gamma$ is necessary to emphasize. It was found that the weight in suggested form does not change the asymptotic form of Shannon, Renyi, Tsallis and Fisher entropies, but change the constants. The main term in weighted Fisher Information is changed by some constant which depend on distance between the true frequency and the value we want to emphasize. In third part we derived the weighted versions of Rao-Cram\'er, Bhattacharyya and Kullback inequalities. This result is applied to the Bayesian problem described above. The asymptotic forms of these inequalities are obtained for a particular class of weight functions., Comment: 33 pages

We analyse an analog of the entropy-power inequality for the weighted entropy., Comment: 17 pages, 2 figures

How do households cope with increases in food prices? How have their eating habits changed in the face of food price volatility? These case studies form part of the second year of Oxfam–IDS research project Life in a Time of Food Price Volatility, which examines how food price volatility affects everyday life in 10 low- and middle-income countries. They examine food prices and how people are eating in five of those countries: Bangladesh, Burkina Faso, Kenya, Pakistan and Vietnam, providing first-hand accounts from participant households. For many, increased food prices means adjusting food consumption downwards, both in quantity and quality, which has a wider effect on wellbeing. Three of these case studies take a broader view of food price increases in Bangladesh, Kenya and Pakistan in 2013, and show that politics and policies have a significant impact on prices. Governments can directly – for good or ill – influence the wellbeing of the poor through decisions on policy instruments such as taxation and levels of subsidies. The research is funded by the UK Government and Irish Aid. Read the global reports from year one of the project, Squeezed, and year two, Help Yourself!

We study an epidemic propagation between $M$ population centra. The novelty of the model is in analyzing the migration of host (remaining in the same centre) and guest (migrated to another centre) populations separately. Even in the simplest case $M=2$, this modification is justified because it gives a more realistic description of migration processes. This becomes evident in a purely migration model with vanishing epidemic parameters. It is important to account for a certain number of guest susceptible present in non-host cenrta because these susceptible may be infected and return to the host node as infectives. The flux of such infectives is not negligible and is comparable with the flux of host infectives migrated to other centra, because the return rate of a guest individual will, by nature, tend to be high. It is shown that taking account of both fluxes of infectives noticeably increases the speed of epidemic spread in a 1D lattice of identical SIR centra., Comment: 19 pages, 2 figures

We present an axiomatic approach to earthquake forecasting in terms of multi-component random fields on a lattice. This approach provides a method for constructing point estimates and confidence intervals for conditional probabilities of strong earthquakes under conditions on the levels of precursors. Also, it provides an approach for setting multilevel alarm system and hypothesis testing for binary alarms. We use a method of comparison for different earthquake forecasts in terms of the increase of Shannon information. 'Forecasting' and 'prediction' of earthquakes are equivalent in this approach., Comment: 21 pages

This paper continues the work Y. Suhov, M. Kelbert. FK-DLR states of a quantum bose-gas, arXiv:1304.0782 [math-ph], and focuses on infinite-volume bosonic states for a quantum system (a quantum gas) in a plane. We work under similar assumptions upon the form of local Hamiltonians and the type of the (pair) interaction potential as in the reference above. The result of the paper is that any infinite-volume FK-DLR functional corresponding to the Hamiltonians is shift-invariant, regardless of whether this functional is unique or not., Comment: 31 pages

The paper focuses on infinite-volume bosonic states for a quantum particle system (a quantum gas) in a Euclidean space. The kinetic energy part of the Hamiltonian is the standard Laplacian (with a Dirichlet's boundary condition at the border of a `box'). The particles interact with each other through a two-body finite-range potential depending on the distance between them and featuring a hard core of a positive diameter. We introduce a class of so-called FK-DLR functionals containing all limiting Gibbs states of the system. In the next paper we will prove that any FK-DLR functional is shift-invariant, regardless of whether it is unique or not., Comment: 32 pages