Some basic notions of first-order unification theory

This report does not contain much novel material, but collects the basic notions and the most frequently used lemmata and theorems of first order unification theory. It is restricted to the case of free terms (i.e. no defining equations)

Unification in Abelian Semigroups

Unification in equational theories, i.e. solving of equations in varieties, is a basic operation in Computational Logic, in Artificial Intelligence (AI) and in many applications of Computer Science. In particular the unification of terms in the presence of an associative and commutative f unction, i.e. solving of equations in Abelian Semigroups, turned out to be of practical relevance for Term Rewriting Systems, Automated Theorem Provers and many AI-programming languages. The observation that unification under associativity and commutativity reduces to the solution of certain linear diophantine equations is the basis for a complete and minimal unification algorithm. The set of most general unifiers is closely related to the notion of a basis for the linear solution space of these equations. These results are extended to unification in free term algebras combined with Abelian Semigroups

Ordinal pattern dependence as a multivariate dependence measure

In this article, we show that the recently introduced ordinal pattern dependence fits into the axiomatic framework of general multivariate dependence measures. Furthermore, we consider multivariate generalizations of established univariate dependence measures like Kendall's $\tau$, Spearman's $\rho$ and Pearson's correlation coefficient. Among these, only multivariate Kendall's $\tau$ proves to take the dynamical dependence of random vectors stemming from multidimensional time series into account. Consequently, the article focuses on a comparison of ordinal pattern dependence and multivariate Kendall's $\tau$. To this end, limit theorems for multivariate Kendall's $\tau$ are established under the assumption of near epoch dependent, data-generating time series. We analyze how ordinal pattern dependence compares to multivariate Kendall's $\tau$ and Pearson's correlation coefficient on theoretical grounds. Additionally, a simulation study illustrates differences in the kind of dependencies that are revealed by multivariate Kendall's $\tau$ and ordinal pattern dependence

Temperature and precipitation extremes in century-long gridded observations, reanalyses, and atmospheric model simulations

Knowledge about long-term changes in climate extremes is vital to better understand multidecadal climate variability and long-term changes and to place today’s extreme events in a historical context. While global changes in temperature and precipitation extremes since the midtwentieth century are well studied, knowledge about century-scale changes is limited. This paper analyses a range of largely independent observations-based data sets covering 1901–2010 for long-term changes and interannual variability in daily scale temperature and precipitation extremes. We compare across data sets for consistency to ascertain our confidence in century-scale changes in extremes. We find consistent warming trends in temperature extremes globally and in most land areas over the past century. For precipitation extremes we find global tendencies toward more intense rainfall throughout much of the twentieth century; however, local changes are spatially more variable. While global time series of the different data sets agree well after about 1950, they often show different changes during the first half of the twentieth century. In regions with good observational coverage, gridded observations and reanalyses agree well throughout the entire past century. Simulations with an atmospheric model suggest that ocean temperatures and sea ice may explain up to about 50% of interannual variability in the global average of temperature extremes, and about 15% in the global average of moderate precipitation extremes, but local correlations are mostly significant only in low latitudes

LP Solutions of Vectorial Integer Subset Sums - Cryptanalysis of Galbraith\u27s Binary Matrix LWE

We consider Galbraith\u27s space efficient LWE variant, where the $(m \times n)$-matrix $A$ is binary. In this binary case, solving a vectorial subset sum problem over the integers allows for decryption. We show how to solve this problem using (Integer) Linear Programming. Our attack requires only a fraction of a second for all instances in a regime for $m$ that cannot be attacked by current lattice algorithms. E.g.\ we are able to solve 100 instances of Galbraith\u27s small LWE challenge $(n,m) = (256, 400)$ all in a fraction of a second. We also show under a mild assumption that instances with $m \leq 2n$ can be broken in polynomial time via LP relaxation. Moreover, we develop a method that identifies weak instances for Galbraith\u27s large LWE challenge $(n,m)=(256, 640)$

Perspective Taking and Moral Evaluation: Themes from Adam Smith.

When we engage in moral deliberation, we take it upon ourselves to consider our conduct not only from our own perspective, but from the perspectives of others. I take this to be obvious. It is far from obvious, though, what this requirement amounts to. When we consider other people’s perspectives, what is it that we must do? Are we merely obligated to consider how we would feel if we were in their shoes? Or must we imagine how they feel? What reason do we have to consider other people’s perspectives in the first place? And how does doing so affect our moral judgments? In The Theory of Moral Sentiments, Adam Smith presents an account of imaginative perspective taking and moral evaluation that answers these questions. Based on a close reading of Smith’s text, and drawing on recent work in both philosophy and social psychology, I argue that we are required to consider other people’s perspectives in virtue of our status as members in a moral community of independent and mutually accountable equals. We imagine ourselves in other people’s shoes not to experience their feelings, but to determine how they ought to feel. We imagine ourselves in their shoes as part of an effort to find common ground: to construct a shared perspective from which to collectively judge the propriety or impropriety, justice or injustice, of our (and their) conduct. I argue that Smith’s account of imaginative perspective taking leads not to utilitarianism (as is commonly thought), but to a contractualist theory of moral evaluation.PHDPhilosophyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/108724/1/waherold_1.pd

Development of a scoring function for comparing simulated and experimental tumor spheroids

Progress continues in the field of cancer biology, yet much remains to be unveiled regarding the mechanisms of cancer invasion. In particular, complex biophysical mechanisms enable a tumor to remodel the surrounding extracellular matrix (ECM), allowing cells to invade alone or collectively. Tumor spheroids cultured in collagen represent a simplified, reproducible 3D model system, which is sufficiently complex to recapitulate the evolving organization of cells and interaction with the ECM that occur during invasion. Recent experimental approaches enable high resolution imaging and quantification of the internal structure of invading tumor spheroids. Concurrently, computational modeling enables simulations of complex multicellular aggregates based on first principles. The comparison between real and simulated spheroids represents a way to fully exploit both data sources, but remains a challenge. We hypothesize that comparing any two spheroids requires first the extraction of basic features from the raw data, and second the definition of key metrics to match such features. Here, we present a novel method to compare spatial features of spheroids in 3D. To do so, we define and extract features from spheroid point cloud data, which we simulated using Cells in Silico (CiS), a high-performance framework for large-scale tissue modeling previously developed by us. We then define metrics to compare features between individual spheroids, and combine all metrics into an overall deviation score. Finally, we use our features to compare experimental data on invading spheroids in increasing collagen densities. We propose that our approach represents the basis for defining improved metrics to compare large 3D data sets. Moving forward, this approach will enable the detailed analysis of spheroids of any origin, one application of which is informing in silico spheroids based on their in vitro counterparts. This will enable both basic and applied researchers to close the loop between modeling and experiments in cancer research

On the Asymptotic Complexity of Solving LWE

We provide for the first time an asymptotic comparison of all known algorithms for the search version of the Learning with Errors (LWE) problem. This includes an analysis of several lattice-based approaches as well as the combinatorial BKW algorithm. Our analysis of the lattice-based approaches defines a general framework, in which the algorithms of Babai, Lindner-Peikert and several pruning strategies appear as special cases. We show that within this framework, all lattice algorithms achieve the same asymptotic complexity. For the BKW algorithm, we present a refined analysis for the case of only a polynomial number of samples via amplification, which allows for a fair comparison with lattice-based approaches. Somewhat surprisingly, such a small number of samples does not make the asymptotic complexity significantly inferior, but only affects the constant in the exponent. As the main result we obtain that both, lattice-based techniques and BKW with a polynomial number of samples, achieve running time 2^{\bigO(n)} for $n$-dimensional LWE, where we make the constant hidden in the big-\bigO notion explicit as a simple and easy to handle function of all LWE-parameters. In the lattice case this function also depends on the time to compute a BKZ lattice basis with block size $\Theta(n)$. Thus, from a theoretical perspective our analysis reveals how LWE\u27s complexity changes as a function of the LWE-parameters, and from a practical perspective our analysis is a useful tool to choose LWE-parameters resistant to all known attacks