Young researchers of the Barents Region

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The Biequivalence of Locally Cartesian Closed Categories and Martin-L\"of Type Theories

Seely's paper "Locally cartesian closed categories and type theory" contains a well-known result in categorical type theory: that the category of locally cartesian closed categories is equivalent to the category of Martin-L\"of type theories with Pi-types, Sigma-types and extensional identity types. However, Seely's proof relies on the problematic assumption that substitution in types can be interpreted by pullbacks. Here we prove a corrected version of Seely's theorem: that the B\'enabou-Hofmann interpretation of Martin-L\"of type theory in locally cartesian closed categories yields a biequivalence of 2-categories. To facilitate the technical development we employ categories with families as a substitute for syntactic Martin-L\"of type theories. As a second result we prove that if we remove Pi-types the resulting categories with families are biequivalent to left exact categories.Comment: TLCA 2011 - 10th Typed Lambda Calculi and Applications, Novi Sad : Serbia (2011

Comparing anomaly detection methods in computer networks

This work in progress outlines a comparison of anomaly detection methods that we are undertaking. We are comparing different types of anomaly detection methods with the purpose of achieving results covering a broad spectrum of anomalies. We also outline the datasets that we will be using and the metrics that we will use for our evaluation

The maximum of Brownian motion with parabolic drift

We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. We give series expansions and integral formulas for the distribution and the first two moments, together with numerical values to high precision.Comment: 37 page

Randomness Relative to Cantor Expansions

Imagine a sequence in which the first letter comes from a binary alphabet, the second letter can be chosen on an alphabet with 10 elements, the third letter can be chosen on an alphabet with 3 elements and so on. When such a sequence can be called random? In this paper we offer a solution to the above question using the approach to randomness proposed by Algorithmic Information Theory.Comment: several small change

Business Survey Data: Do They Help in Forecasting the Macro Economy?

In this paper we examine whether data from business tendency surveys are useful for forecasting the macro economy in the short run. Our analyses primarily concern the growth rates of real GDP but we also evaluate forecasts of other variables such as unemployment, price and wage inflation, interest rates, and exchange-rate changes. The starting point is a so-called dynamic factor model (DFM), which is used both as a framework for dimension reduction in forecasting and as a procedure for filtering out unimportant idiosyncratic noise in the underlying survey data. In this way, it is possible to model a rather large number of noise-reduced survey variables in a parsimoniously parameterised vector autoregression (VAR). To assess the forecasting performance of the procedure, comparisons are made with VARs that either use the survey variables directly, are based on macro variables only, or use other popular summary indices of economic activity. As concerns forecasts of GDP growth, the procedure turns out to outperform the competing alternatives in most cases. For the other macro variables, the evidence is more mixed, suggesting in particular that there often is little difference between the DFM-based indicators and the popular summary indices of economic activity.Business survey data; Dynamic factor models; Macroeconomic forecasting

Dependent Types for Pragmatics

This paper proposes the use of dependent types for pragmatic phenomena such as pronoun binding and presupposition resolution as a type-theoretic alternative to formalisms such as Discourse Representation Theory and Dynamic Semantics.Comment: This version updates the paper for publication in LEU