Tarski monoids: Matui's spatial realization theorem

We introduce a class of inverse monoids, called Tarski monoids, that can be regarded as non-commutative generalizations of the unique countable, atomless Boolean algebra. These inverse monoids are related to a class of etale topological groupoids under a non-commutative generalization of classical Stone duality and, significantly, they arise naturally in the theory of dynamical systems as developed by Matui. We are thereby able to reinterpret a theorem of Matui on a class of \'etale groupoids as an equivalent theorem about a class of Tarski monoids: two simple Tarski monoids are isomorphic if and only if their groups of units are isomorphic. The inverse monoids in question may also be viewed as countably infinite generalizations of finite symmetric inverse monoids. Their groups of units therefore generalize the finite symmetric groups and include amongst their number the classical Thompson groups.Comment: arXiv admin note: text overlap with arXiv:1407.147

An asymptotic bound for secant varieties of Segre varieties

This paper studies the defectivity of secant varieties of Segre varieties. We prove that there exists an asymptotic lower estimate for the greater non-defective secant variety (without filling the ambient space) of any given Segre variety. In particular, we prove that the ratio between the greater non-defective secant variety of a Segre variety and its expected rank is lower bounded by a value depending just on the number of factors of the Segre variety. Moreover, in the final section, we present some results obtained by explicit computation, proving the non-defectivity of all the secant varieties of Segre varieties of the shape (P^n)^4, with 1 < n < 11, except at most \sigma_199((P^8)^4) and \sigma_357((P^10)^4).Comment: 14 page

Poisson sigma models and symplectic groupoids

We consider the Poisson sigma model associated to a Poisson manifold. The perturbative quantization of this model yields the Kontsevich star product formula. We study here the classical model in the Hamiltonian formalism. The phase space is the space of leaves of a Hamiltonian foliation and has a natural groupoid structure. If it is a manifold then it is a symplectic groupoid for the given Poisson manifold. We study various families of examples. In particular, a global symplectic groupoid for a general class of two-dimensional Poisson domains is constructed.Comment: 34 page

Neural ensemble decoding reveals a correlate of viewer- to object-centered spatial transformation in monkey parietal cortex

The parietal cortex contains representations of space in multiple coordinate systems including retina-, head-, body-, and world-based systems. Previously, we found that when monkeys are required to perform spatial computations on objects, many neurons in parietal area 7a represent position in an object-centered coordinate system as well. Because visual information enters the brain in a retina-centered reference frame, generation of an object-centered reference requires the brain to perform computation on the visual input. We provide evidence that area 7a contains a correlate of that computation. Specifically, area 7a contains neurons that code information in retina- and object-centered coordinate systems. The information in retina-centered coordinates emerges first, followed by the information in object-centered coordinates. We found that the strength and accuracy of these representations is correlated across trials. Finally, we found that retina-centered information could be used to predict subsequent object-centered signals, but not vice versa. These results are consistent with the hypothesis that either area 7a, or an area that precedes area 7a in the visual processing hierarchy, is performing the retina- to object-centered transformation

Culture Positive Brucella Endocarditis in a Case of Baloon Mitral Valvotomy

Brucella endocarditis is a rare condition which occurs as a focal complication in chronic brucellosis cases. We report a rare brucella endocarditis case in a RVHD patient. A 26 years old male was admitted with fever on off for almost one year. The blood culture yielded growth of Brucella melitensis after ten days of incubation. Isolated colonies were reconfirmed as Brucella species by PCR study. Patient’s serum tested positive for brucella slide agglutination test and STAT titer was 640IU. Echocardiography showed vegetation on mitral valve. Patient was treated with both medical and surgical intervention. After chemotherapy, patient’s blood culture was sterile, slide agglutination & STAT (40IU) were negative. Repeat echocardiography showed no fresh vegetation. Considering high mortality rate (80%) in Brucella endocarditis, it is very important for clinicians to suspect it. Prompt antibiotic therapy and surgical intervention is life saving in fatal cases

First-principles study of H intercalation in rutile TiO2

Published versio

Strong inapproximability of the shortest reset word

The \v{C}ern\'y conjecture states that every $n$-state synchronizing automaton has a reset word of length at most $(n-1)^2$. We study the hardness of finding short reset words. It is known that the exact version of the problem, i.e., finding the shortest reset word, is NP-hard and coNP-hard, and complete for the DP class, and that approximating the length of the shortest reset word within a factor of $O(\log n)$ is NP-hard [Gerbush and Heeringa, CIAA'10], even for the binary alphabet [Berlinkov, DLT'13]. We significantly improve on these results by showing that, for every $\epsilon>0$, it is NP-hard to approximate the length of the shortest reset word within a factor of $n^{1-\epsilon}$. This is essentially tight since a simple $O(n)$-approximation algorithm exists.Comment: extended abstract to appear in MFCS 201

Effect of Neem Oil on Sperm Mitochondrial Activity

It is a known fact that neem oil has some effect on motility of sperm. Motility of sperm depends on mitochondrial activity present in mid-piece of sperm. In the present study, the mitochondrial activity of sperm was evaluated after treating semen with the different quantities of neem oil. The mitochondrial activity was also evaluated after subjecting the semen samples for different incubation periods keeping the quantity of semen as well as that of neem oil same. Tests were done on thirty normozoospermic semen samples with motile score more than 75%. It was found that as the quantity of neem oil increases, the mitochondrial activity decreases significantly (P < 0.001). Similar results were found, when same quantity of neem oil was treated with same quantity of semen, but incubating for different time durations. The mitochondrial activity decreases significantly (P < 0.001) from one minute to twenty minutes. So, it indicates that as the contact period between neem oil and semen increases the mitochondrial activity decreases significantl

Studies on vibration of some rib-stiffened cantilever plates

The vibrational mode shapes and frequencies of rib-stiffened skew cantilever plates as determined by holographic interferometry are given. The effects of varying the sweep back angle, rib stiffness and aspect ratio are studied along with the influence of varying the boundary conditions at the root chord on the vibrational behavior of the plates. The study is applicable to investigating the vibrational behavior of stiffened plates often used in the design of guided rockets and missiles