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In the propositional modal (and algebraic) treatment of two-variable first-order logic equality is modelled by a `diagonal' constant, interpreted in square products of universal frames as the identity (also known as the `diagonal')…
We consider the problem of designing an optimal quantum detector with a fixed rate of inconclusive results that maximizes the probability of correct detection, when distinguishing between a collection of mixed quantum states. We develop a…
Within the machine learning community, the widely-used uniform convergence framework has been used to answer the question of how complex, over-parameterized models can generalize well to new data. This approach bounds the test error of the…
The efficiency statistics of a small thermodynamic machine has been recently investigated assuming that the total dissipation was a linear combination of two currents: the input and output currents. Here, we relax this standard assumption…
If an experimentalist observes a sequence of emitted quantum states via either projective or positive-operator-valued measurements, the outcomes form a time series. Individual time series are realizations of a stochastic process over the…
League competition is investigated using random processes and scaling techniques. In our model, a weak team can upset a strong team with a fixed probability. Teams play an equal number of head-to-head matches and the team with the largest…
This study proposes a mathematical model to optimally locate a set of detectors in such a way that the expected number of casualties in a given threat area can be minimized. Detectors may not be perfectly reliable, which is often a function…
Unreplicated two-level factorial designs are often used in screening experiments to determine which factors out of a large plausible set are active. A theorem regarding the generalized word count pattern is stated and proved for…
We propose confidence sequences -- sequences of confidence intervals which are valid uniformly over time -- for quantiles of any distribution over a complete, fully-ordered set, based on a stream of i.i.d. observations. We give methods both…
We present the first solution to the problem of estimation of the state of multimachine power systems with lossy transmission lines. We consider the classical three-dimensional \fluxdecay" model of the power system and assume that the…
The detectors in mass spectrometers are precise enough to count ion events. In practice, the statistics of chemical noise are affected by large quantization errors and overdispersion because of amplification in the detector. The detector…
Several interesting generative learning algorithms involve a complex probability distribution over many random variables, involving intractable normalization constants or latent variable normalization. Some of them may even not have an…
Motivated by real-world machine learning applications, we consider a statistical classification task in a sequential setting where test samples arrive sequentially. In addition, the generating distributions are unknown and only a set of…
Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in…
The best arm identification problem (BEST-1-ARM) is the most basic pure exploration problem in stochastic multi-armed bandits. The problem has a long history and attracted significant attention for the last decade. However, we do not yet…
This thesis is concerned with the quantitative assessment of security in software. More specifically, it tackles the problem of efficient computation of channel capacity, the maximum amount of confidential information leaked by software,…
This paper implements the Deep Deterministic Policy Gradient (DDPG) algorithm for computing optimal policies for partially observable single-product periodic review inventory control problems with setup costs and backorders. The decision…
The optimal (`equilibrium') macroscopic properties of an economy with $N$ industries endowed with different technologies, $P$ commodities and one consumer are derived in the limit $N\to\infty$ with $n=N/P$ fixed using the replica method.…
We study a class of optimal allocation problems, including the well-known Bomber Problem, with the following common probabilistic structure. An aircraft equipped with an amount~$x$ of ammunition is intercepted by enemy airplanes arriving…
Recent advances on overfitting Bayesian mixture models provide a solid and straightforward approach for inferring the underlying number of clusters and model parameters in heterogeneous datasets. The applicability of such a framework in…