PAC-Bayes Unleashed: Generalisation Bounds with Unbounded Losses

We present new PAC-Bayesian generalisation bounds for learning problems with unbounded loss functions. This extends the relevance and applicability of the PAC-Bayes learning framework, where most of the existing literature focuses on supervised learning problems with a bounded loss function (typically assumed to take values in the interval [0;1]). In order to relax this classical assumption, we propose to allow the range of the loss to depend on each predictor. This relaxation is captured by our new notion of HYPothesis-dependent rangE (HYPE). Based on this, we derive a novel PAC-Bayesian generalisation bound for unbounded loss functions, and we instantiate it on a linear regression problem. To make our theory usable by the largest audience possible, we include discussions on actual computation, practicality and limitations of our assumptions.

Fusion of interfaces in Landau-Ginzburg models: a functorial approach

We investigate the fusion of B-type interfaces in two-dimensional supersymmetric Landau-Ginzburg models. In particular, we propose to describe the fusion of an interface in terms of a fusion functor that acts on the category of modules of the underlying polynomial rings of chiral superfields. This uplift of a functor on the category of matrix factorisations simplifies the actual computation of interface fusion. Besides a brief discussion of minimal models, we illustrate the power of this approach in the SU(3)/U(2) Kazama-Suzuki model where we find fusion functors for a set of elementary topological defects from which all rational B-type topological defects can be generated.

Input-Output Models and Derived Indicators: A Critical Review

Input-Output literature can be characterized as complicated and chaotic. The complications concern the nomenclature of concepts for the derived indices from the multipliers’ models, their mathematical expressions and computable applications. The terminologies’ inconsistencies often end up to a deviation between the description for these indices and their actual computation, or/and to a misunderstanding as for their usefulness and outcomes. The aim of the paper is to help the readers to face the weaknesses in the literature. In this way, the paper provide an overview with a critical look to the constructed multipliers’ matrices and their derived indicators from the I-O models, and elaborate the causes for the scrutinized confusions. The paper proposes both terminological and computational adjustments and differentiated approaches for the models and their indices, in order to ameliorate their capabilities and to exploit their peculiarities for the developmental patterns. Alternative interpretative ways and applicable expansions are suggested.

The Analysis of Reproduction in Population of the Slovak Spotted Dairy Cows

The aim of study was to analyse the reproduction and factors affecting on reproduction traits of dairy cows in population of Slovak Spotted cattle from 2007 to 2016 the results for 37,274 dairy cows: days to first service (DFS), days open (DO), number of inseminations per conception (NIC), age of first calving (AFC) and calving interval (CI). The basic statistical analysis were analysed using the SAS version 9.3. For the actual computation a linear models with fixed effects was used: For the actual computation a linear models with fixed effects was used: yijklm = μ + HYSi + BTj+ Fk+ Bl +eijklm. The linear model represents coefficients determination R2 = 0.452117% (P < 0.001) for DFS, R2 = 0.377715% (P < 0.001) for DO, R2 = 0.348442% (P < 0.001) for NIC and R2 = 0.317128% (P < 0.001) for CI with all fixed effects. Correlation coefficients among DFS with DO, NIC, AFC and CI were r = 0.37275, r = -0.06881, r = 0.06493 and r = 0.08348. These coefficients were highly statistically significant (P < 0.001).

Handling Overruns and Underruns of Real-Time Processes With Precedence and Exclusion Relations Using a Pre-Run-Time Schedule

Many embedded systems applications have hard timing requirements where real-time processes with precedence and exclusion relations must be completed before specified deadlines. This requires that the worst-case computation times of the real-time processes be estimated with sufficient precision during system design, which sometimes can be difficult in practice. If the actual computation time of a real-time process during run-time exceeds the estimated worst-case computation time, an overrun will occur, which may cause the real-time process to not only miss its own deadline, but also cause a cascade of other real-time processes to also miss their deadline, possibly resulting in total system failure. However, if the actual computation time of a real-time process during run-time is less than the estimated worst-case computation time, an underrun will occur, which may result in under-utilization of system resources. This paper describes a method for handling underruns and overruns when scheduling a set of real-time processes with precedence and exclusion relations using a pre-run-time schedule. The technique effectively tracks and utilizes unused processor time resources to reduce the chances of missing real-time process deadlines, thereby providing the capability to significantly increase both system utilization and system robustness in the presence of inaccurate estimates of the worst-case computation times of real-time processes.

Reason as Reckoning: Hobbes's Natural Law as Right Reason

Hobbes conception of reason as computation or reckoning is significantly different in Part I of De Corpore (entitled Computatio sive Logica) from what I take to be the later treatment in Leviathan. In the late actual computation with words starts with making an affirmation, framing a proposition. Reckoning then has to do with the consequences of propositions, or how they connect the facts, states of affairs or actions which they refer tor account. Starting from this it can be made clear how Hobbes understood the crucial application of this conception to natural law, identified as 'right reason'.

Random Boolean expressions

International audience We examine how we can define several probability distributions on the set of Boolean functions on a fixed number of variables, starting from a representation of Boolean expressions by trees. Analytic tools give us a systematic way to prove the existence of probability distributions, the main challenge being the actual computation of the distributions. We finally consider the relations between the probability of a Boolean function and its complexity.

A Stability Criterion for Parameter-Dependent Gyroscopic Systems

A stability criterion for parameter-dependent gyroscopic systems is established and three examples are used to illustrate its application to typical engineering problems. In a number of practical situations, the criterion can be used to predict system stability with little actual computation and without solving any eigenvalue problem or approximating the eigenvalue locus. Thus, the criterion provides designers with a quick and accurate tool for assessing the stability consequences of potential design changes.