Algebraic Unimodular Counting

We study algebraic algorithms for expressing the number of non-negative integer solutions to a unimodular system of linear equations as a function of the right hand side. Our methods include Todd classes of toric varieties via Gr\"obner bases, and rational generating functions as in Barvinok's algorithm. We report polyhedral and computational results for two special cases: counting contingency tables and Kostant's partition function.Comment: 21 page

Not all simplicial polytopes are weakly vertex-decomposable

In 1980 Provan and Billera defined the notion of weak $k$-decomposability for pure simplicial complexes. They showed the diameter of a weakly $k$-decomposable simplicial complex $\Delta$ is bounded above by a polynomial function of the number of $k$-faces in $\Delta$ and its dimension. For weakly 0-decomposable complexes, this bound is linear in the number of vertices and the dimension. In this paper we exhibit the first examples of non-weakly 0-decomposable simplicial polytopes

Fermions in odd space-time dimensions: back to basics

It is a well known feature of odd space-time dimensions $d$ that there exist two inequivalent fundamental representations $A$ and $B$ of the Dirac gamma matrices. Moreover, the parity transformation swaps the fermion fields living in $A$ and $B$. As a consequence, a parity invariant Lagrangian can only be constructed by incorporating both the representations. Based upon these ideas and contrary to long held belief, we show that in addition to a discrete exchange symmetry for the massless case, we can also define chiral symmetry provided the Lagrangian contains fields corresponding to both the inequivalent representations. We also study the transformation properties of the corresponding chiral currents under parity and charge conjugation operations. We work explicitly in 2+1 dimensions and later show how some of these ideas generalize to an arbitrary number of odd dimensions.Comment: 8 pages, no figure

Vibrations on pulse tube based Dry Dilution Refrigerators for low noise measurements

Dry Dilution Refrigerators (DDR) based on pulse tube cryo-coolers have started to replace Wet Dilution Refrigerators (WDR) due to the ease and low cost of operation. However these advantages come at the cost of increased vibrations, induced by the pulse tube. In this work, we present the vibration measurements performed on three different commercial DDRs. We describe in detail the vibration measurement system we assembled, based on commercial accelerometers, conditioner and DAQ, and examined the effects of the various damping solutions utilized on three different DDRs, both in the low and high frequency regions. Finally, we ran low temperature, pseudo-massive (30 and 250 g) germanium bolometers in the best vibration-performing system under study and report on the results

Electroweak Tests at Beta-beams

We explore the possibility of measuring the Weinberg angle from (anti)neutrino-electron scattering using low energy beta beams, a method that produces single flavour neutrino beams from the beta-decay of boosted radioactive ions. We study how the sensitivity of a possible measurement depends on the intensity of the ion beam and on a combination of different Lorentz boosts of the ions.Comment: 10 pages, 6 figure

Sparse solutions of linear Diophantine equations

We present structural results on solutions to the Diophantine system $A{\boldsymbol y} = {\boldsymbol b}$, ${\boldsymbol y} \in \mathbb Z^t_{\ge 0}$ with the smallest number of non-zero entries. Our tools are algebraic and number theoretic in nature and include Siegel's Lemma, generating functions, and commutative algebra. These results have some interesting consequences in discrete optimization

Symmetric discrete coherent states for n qubits

We put forward a method of constructing discrete coherent states for n qubits. After establishing appropriate displacement operators, the coherent states appear as displaced versions of a fiducial vector that is fixed by imposing a number of natural symmetry requirements on its Q-function. Using these coherent states we establish a partial order in the discrete phase space, which allows us to picture some n-qubit states as apparent distributions. We also analyze correlations in terms of sums of squared Q-functions.Comment: Published in J. Phys. A. Special issue on Coherent State

Marianus Scholasticus’ APl 201. A Christian rewriting of Eros from Justin II and Sophia’s reign

The aim of this paper is to perform a deep analysis of APl 201, a fi ve-couplet epigram ascribed in all manuscripts to the almost unknown Marianus Scholasticus. When describing a work of art also unidentifi able, the poet progressively transforms the Eros he (probably) sees in the image of the Christian saviour, by means of a cautious wordplay and a symbolic re-signifi cation of the pagan attributes of that god. Furthermore, some connections between Marianus’ other epigrams and the reign of Justin II and his wife Sophia’s, particularly the last one, come to suggest a commissioned relation of the poet with the imperial couple, in relation to an intentional advertising propaganda that aimed to promote both of them to icons of orthodoxy in the second half of the sixth century AD

Emerging role of angiogenesis in adaptive and maladaptive right ventricular remodeling in pulmonary hypertension

Right ventricular (RV) function is the primary prognostic factor for both morbidity and mortality in pulmonary hypertension (PH). RV hypertrophy is initially an adaptive physiological response to increased overload; however, with persistent and/or progressive afterload increase, this response frequently transitions to more pathological maladaptive remodeling. The mechanisms and disease processes underlying this transition are mostly unknown. Angiogenesis has recently emerged as a major modifier of RV adaptation in the setting of pressure overload. A novel paradigm has emerged that suggests that angiogenesis and angiogenic signaling are required for RV adaptation to afterload increases and that impaired and/or insufficient angiogenesis is a major driver of RV decompensation. Here, we summarize our current understanding of the concepts of maladaptive and adaptive RV remodeling, discuss the current literature on angiogenesis in the adapted and failing RV, and identify potential therapeutic approaches targeting angiogenesis in RV failure