Atomistic subsemirings of the lattice of subspaces of an algebra

Let A be an associative algebra with identity over a field k. An atomistic subsemiring R of the lattice of subspaces of A, endowed with the natural product, is a subsemiring which is a closed atomistic sublattice. When R has no zero divisors, the set of atoms of R is endowed with a multivalued product. We introduce an equivalence relation on the set of atoms such that the quotient set with the induced product is a monoid, called the condensation monoid. Under suitable hypotheses on R, we show that this monoid is a group and the class of k1_A is the set of atoms of a subalgebra of A called the focal subalgebra. This construction can be iterated to obtain higher condensation groups and focal subalgebras. We apply these results to G-algebras for G a group; in particular, we use them to define new invariants for finite-dimensional irreducible projective representations.Comment: 14 page

Using A Nameserver to Enhance Control System Efficiency

The Thomas Jefferson National Accelerator Facility (Jefferson Lab) control system uses a nameserver to reduce system response time and to minimize the impact of client name resolution on front-end computers. The control system is based on the Experimental Physics and Industrial Control System (EPICS), which uses name-based broadcasts to initiate data communication. By default, when EPICS process variables (PV) are requested by client applications, all front-end computers receive the broadcasts and perform name resolution processing against local channel name lists. The nameserver is used to offload the name resolution task to a single node. This processing, formerly done on all front-end computers, is now done only by the nameserver. In a control system with heavily loaded front-end computers and high peak client connection loads, a significant performance improvement is seen. This paper describes the name server in more detail, and discusses the strengths and weaknesses of making name resolution a centralized service.Comment: ICALEPCS 200

(SL(N),q)(SL(N),q)-opers, the qq-Langlands correspondence, and quantum/classical duality

A special case of the geometric Langlands correspondence is given by the relationship between solutions of the Bethe ansatz equations for the Gaudin model and opers - connections on the projective line with extra structure. In this paper, we describe a deformation of this correspondence for $SL(N)$. We introduce a difference equation version of opers called $q$-opers and prove a $q$-Langlands correspondence between nondegenerate solutions of the Bethe ansatz equations for the XXZ model and nondegenerate twisted $q$-opers with regular singularities on the projective line. We show that the quantum/classical duality between the XXZ spin chain and the trigonometric Ruijsenaars-Schneider model may be viewed as a special case of the $q$-Langlands correspondence. We also describe an application of $q$-opers to the equivariant quantum $K$-theory of the cotangent bundles to partial flag varieties.Comment: v3: 32 pages, 2 figures; minor revisions, to appear in Commun. Math. Phy

Isomonodromic deformations of connections with singularities of parahoric formal type

In previous work, the authors have developed a geometric theory of fundamental strata to study connections on the projective line with irregular singularities of parahoric formal type. In this paper, the moduli space of connections that contain regular fundamental strata with fixed combinatorics at each singular point is constructed as a smooth Poisson reduction. The authors then explicitly compute the isomonodromy equations as an integrable system. This result generalizes work of Jimbo, Miwa, and Ueno to connections whose singularities have parahoric formal type.Comment: 32 pages. One of the main theorems (Theorem 5.1) has been significantly strengthened. It now states that the isomonodromy equations give rise to an integrable system on the moduli space of framed connections with fixed combinatorics instead of only on a principal GL_n bundle over this space. Sections 5 and 6 have been substantially rewritte

The spreading of SARS-CoV-2: Interage contacts and networks degree distribution

Notable cross-country differences exist in the diffusion of the Covid-19 and in its lethality. Contact patterns in populations, and in particular intergenerational contacts, have been argued to be responsible for the most vulnerable, the elderly, getting infected more often and thus driving up mortality in some context, like in the southern European one. This paper asks a simple question: is it between whom contacts occur that matters or is it simply how many contacts people have? Due to the high number of confounding factors, it is extremely difficult to empirically assess the impact of single network features separately. This is why we rely on a simulation exercise in which we counterfactually manipulate single aspects of countries’ age distribution and network structures. We disentangle the contributions of the kind and of the number of contacts while holding constant the age structure. More precisely, we isolate the respective effects of inter-age contact patterns, degree distribution and clustering on the virus propagation across age groups. We use survey data on face-to-face contacts for Great Britain, Italy, and Germany, to reconstruct networks that mirror empirical contact patterns in these three countries. It turns out that the number of social contacts (degree distribution) largely accounts for the higher infection rates of the elderly in the Italian context, while differences in inter-age contacts patterns are only responsible for minor differences. This suggests that policies specifically targeting inter-age contacts would be little effective

Evaluation of bait acceptance by wild boar and non-target species - test of different distribution modalities and seasonal variations - implication for oral vaccination efficiency against classical swine fever virus

Sage, M., Hubert, P., Rossi, S

Inelastic collisions of ultra-cold heteronuclear molecules in an optical trap

Ultra-cold RbCs molecules in high-lying vibrational levels of the a$^3\Sigma^+$ ground electronic state are confined in an optical trap. Inelastic collision rates of these molecules with both Rb and Cs atoms are determined for individual vibrational levels, across an order of magnitude of binding energies. A simple model for the collision process is shown to accurately reproduce the observed scattering rates

The Cool ISM in S0 Galaxies. I. A Survey of Molecular Gas

Lenticular galaxies remain remarkably mysterious as a class. Observations to date have not led to any broad consensus about their origins, properties and evolution, though they are often thought to have formed in one big burst of star formation early in the history of the Universe, and to have evolved relatively passively since then. In that picture, current theory predicts that stellar evolution returns substantial quantities of gas to the interstellar medium; most is ejected from the galaxy, but significant amounts of cool gas might be retained. Past searches for that material, though, have provided unclear results. We present results from a survey of molecular gas in a volume-limited sample of field S0 galaxies, selected from the Nearby Galaxies Catalog. CO emission is detected from 78 percent of the sample galaxies. We find that the molecular gas is almost always located inside the central few kiloparses of a lenticular galaxy, meaning that in general it is more centrally concentrated than in spirals. We combine our data with HI observations from the literature to determine the total masses of cool and cold gas. Curiously, we find that, across a wide range of luminosity, the most gas rich galaxies have about 10 percent of the total amount of gas ever returned by their stars. That result is difficult to understand within the context of either monolithic or hierarchical models of evolution of the interstellar medium.Comment: 26 pages of text, 15 pages of tables, 10 figures. Accepted for publication in the Astrophysical Journa

Cyclin D-Cdk4,6 Drives Cell-Cycle Progression via the Retinoblastoma Protein's C-Terminal Helix.

The cyclin-dependent kinases Cdk4 and Cdk6 form complexes with D-type cyclins to drive cell proliferation. A well-known target of cyclin D-Cdk4,6 is the retinoblastoma protein Rb, which inhibits cell-cycle progression until its inactivation by phosphorylation. However, the role of Rb phosphorylation by cyclin D-Cdk4,6 in cell-cycle progression is unclear because Rb can be phosphorylated by other cyclin-Cdks, and cyclin D-Cdk4,6 has other targets involved in cell division. Here, we show that cyclin D-Cdk4,6 docks one side of an alpha-helix in the Rb C terminus, which is not recognized by cyclins E, A, and B. This helix-based docking mechanism is shared by the p107 and p130 Rb-family members across metazoans. Mutation of the Rb C-terminal helix prevents its phosphorylation, promotes G1 arrest, and enhances Rb's tumor suppressive function. Our work conclusively demonstrates that the cyclin D-Rb interaction drives cell division and expands the diversity of known cyclin-based protein docking mechanisms

Opers on the projective line, Wronskian relations, and the Bethe Ansatz

It is well-known that the spectra of the Gaudin model may be described in terms of solutions of the Bethe Ansatz equations. A conceptual explanation for the appearance of the Bethe Ansatz equations is provided by appropriate $G$-opers: $G$-connections on the projective line with extra structure. In fact, solutions of the Bethe Ansatz equations are parameterized by an enhanced version of opers called Miura opers; here, the opers appearing have only regular singularities. Feigin, Frenkel, Rybnikov, and Toledano Laredo have introduced an inhomogeneous version of the Gaudin model; this model incorporates an additional twist factor, which is an element of the Lie algebra of $G$. They exhibited the Bethe Ansatz equations for this model and gave a geometric interpretation of the spectra in terms of opers with an irregular singularity. In this paper, we consider a new approach to the study of the spectra of the inhomogeneous Gaudin model in terms of a further enhancement of opers called twisted Miura-Pl\"ucker opers and a certain system of nonlinear differential equations called the $qq$-system. We show that there is a close relationship between solutions of the inhomogeneous Bethe Ansatz equations and polynomial solutions of the $qq$-system and use this fact to construct a bijection between the set of solutions of the inhomogeneous Bethe Ansatz equations and the set of nondegenerate twisted Miura-Pl\"ucker opers. We further prove that as long as certain combinatorial conditions are satisfied, nondegenerate twisted Miura-Pl\"ucker opers are in fact Miura opers.Comment: 38 pages, revised versio