Partial rescue of retinal function in chronically hypoglycemic mice

Purpose. Mice rendered hypoglycemic by a null mutation in the glucagon receptor gene Gcgr display late-onset retinal degeneration and loss of retinal sensitivity. Acute hyperglycemia induced by dextrose ingestion does not restore their retinal function, which is consistent with irreversible loss of vision. The goal of this study was to establish whether long-term administration of high dietary glucose rescues retinal function and circuit connectivity in aged Gcgr−/− mice. Methods. Gcgr−/− mice were administered a carbohydrate-rich diet starting at 12 months of age. After 1 month of treatment, retinal function and structure were evaluated using electroretinographic (ERG) recordings and immunohistochemistry. Results. Treatment with a carbohydrate-rich diet raised blood glucose levels and improved retinal function in Gcgr−/− mice. Blood glucose increased from moderate hypoglycemia to euglycemic levels, whereas ERG b-wave sensitivity improved approximately 10-fold. Because the b-wave reflects the electrical activity of second-order cells, we examined for changes in rod-to-bipolar cell synapses. Gcgr−/− retinas have 20% fewer synaptic pairings than Gcgr+/− retinas. Remarkably, most of the lost synapses were located farthest from the bipolar cell body, near the distal boundary of the outer plexiform layer (OPL), suggesting that apical synapses are most vulnerable to chronic hypoglycemia. Although treatment with the carbohydrate-rich diet restored retinal function, it did not restore these synaptic contacts. Conclusions. Prolonged exposure to diet-induced euglycemia improves retinal function but does not reestablish synaptic contacts lost by chronic hypoglycemia. These results suggest that retinal neurons have a homeostatic mechanism that integrates energetic status over prolonged periods of time and allows them to recover functionality despite synaptic loss.

On some solutions of a functional equation related to the partial sums of the Riemann zeta function

In this paper, we prove that infinite-dimensional vector spaces of α-dense curves are generated by means of the functional equations f(x)+f(2x)+⋯+f(nx)=0, with n≥2, which are related to the partial sums of the Riemann zeta function. These curves α-densify a large class of compact sets of the plane for arbitrary small α, extending the known result that this holds for the cases n=2,3. Finally, we prove the existence of a family of solutions of such functional equation which has the property of quadrature in the compact that densifies, that is, the product of the length of the curve by the nth power of the density approaches the Jordan content of the compact set which the curve densifies.

A note on the real projection of the zeros of partial sums of Riemann zeta function

This paper proves that the real projection of each simple zero of any partial sum of the Riemann zeta function ζn(s):=∑nk=11ks,n>2 , is an accumulation point of the set {Res : ζ n (s) = 0}.

Computing the zeros of the partial sums of the Riemann zeta function

In this paper, we introduce a formula for the exact number of zeros of every partial sum of the Riemann zeta function inside infinitely many rectangles of the critical strips where they are situated.

Comparative study of RPSALG algorithm for convex semi-infinite programming

The Remez penalty and smoothing algorithm (RPSALG) is a unified framework for penalty and smoothing methods for solving min-max convex semi-infinite programing problems, whose convergence was analyzed in a previous paper of three of the authors. In this paper we consider a partial implementation of RPSALG for solving ordinary convex semi-infinite programming problems. Each iteration of RPSALG involves two types of auxiliary optimization problems: the first one consists of obtaining an approximate solution of some discretized convex problem, while the second one requires to solve a non-convex optimization problem involving the parametric constraints as objective function with the parameter as variable. In this paper we tackle the latter problem with a variant of the cutting angle method called ECAM, a global optimization procedure for solving Lipschitz programming problems. We implement different variants of RPSALG which are compared with the unique publicly available SIP solver, NSIPS, on a battery of test problems.

Real-time 3D semi-local surface patch extraction using GPGPU

Feature vectors can be anything from simple surface normals to more complex feature descriptors. Feature extraction is important to solve various computer vision problems: e.g. registration, object recognition and scene understanding. Most of these techniques cannot be computed online due to their complexity and the context where they are applied. Therefore, computing these features in real-time for many points in the scene is impossible. In this work, a hardware-based implementation of 3D feature extraction and 3D object recognition is proposed to accelerate these methods and therefore the entire pipeline of RGBD based computer vision systems where such features are typically used. The use of a GPU as a general purpose processor can achieve considerable speed-ups compared with a CPU implementation. In this work, advantageous results are obtained using the GPU to accelerate the computation of a 3D descriptor based on the calculation of 3D semi-local surface patches of partial views. This allows descriptor computation at several points of a scene in real-time. Benefits of the accelerated descriptor have been demonstrated in object recognition tasks. Source code will be made publicly available as contribution to the Open Source Point Cloud Library.

Robust linear semi-infinite programming duality under uncertainty

In this paper, we propose a duality theory for semi-infinite linear programming problems under uncertainty in the constraint functions, the objective function, or both, within the framework of robust optimization. We present robust duality by establishing strong duality between the robust counterpart of an uncertain semi-infinite linear program and the optimistic counterpart of its uncertain Lagrangian dual. We show that robust duality holds whenever a robust moment cone is closed and convex. We then establish that the closed-convex robust moment cone condition in the case of constraint-wise uncertainty is in fact necessary and sufficient for robust duality. In other words, the robust moment cone is closed and convex if and only if robust duality holds for every linear objective function of the program. In the case of uncertain problems with affinely parameterized data uncertainty, we establish that robust duality is easily satisfied under a Slater type constraint qualification. Consequently, we derive robust forms of the Farkas lemma for systems of uncertain semi-infinite linear inequalities.

Calmness modulus of linear semi-infinite programs

Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound on the calmness modulus for semi-infinite programs with unique optimal solution which turns out to be the exact modulus when the problem is finitely constrained. The relationship between the calmness of the argmin mapping and the same property for the (sub)level set mapping (with respect to the objective function), for semi-infinite programs and without requiring the uniqueness of the nominal solution, is explored, too, providing an upper bound on the calmness modulus of the argmin mapping. When confined to finitely constrained problems, we also provide a computable upper bound as it only relies on the nominal data and parameters, not involving elements in a neighborhood. Illustrative examples are provided.

Mathematical programming model for heat exchanger design through optimization of partial objectives

Mathematical programming can be used for the optimal design of shell-and-tube heat exchangers (STHEs). This paper proposes a mixed integer non-linear programming (MINLP) model for the design of STHEs, following rigorously the standards of the Tubular Exchanger Manufacturers Association (TEMA). Bell–Delaware Method is used for the shell-side calculations. This approach produces a large and non-convex model that cannot be solved to global optimality with the current state of the art solvers. Notwithstanding, it is proposed to perform a sequential optimization approach of partial objective targets through the division of the problem into sets of related equations that are easier to solve. For each one of these problems a heuristic objective function is selected based on the physical behavior of the problem. The global optimal solution of the original problem cannot be ensured even in the case in which each of the sub-problems is solved to global optimality, but at least a very good solution is always guaranteed. Three cases extracted from the literature were studied. The results showed that in all cases the values obtained using the proposed MINLP model containing multiple objective functions improved the values presented in the literature.

The Zeros of Riemann Zeta Partial Sums Yield Solutions to f(x) + f(2x) + · · · + f(nx) = 0

This paper proves that every zero of any n th , n ≥ 2, partial sum of the Riemann zeta function provides a vector space of basic solutions of the functional equation f(x)+f(2x)+⋯+f(nx)=0,x∈R . The continuity of the solutions depends on the sign of the real part of each zero.

Community attributes determine facilitation potential in a semi-arid steppe

Studies on positive plant–plant relations have traditionally focused on pair-wise interactions. Conversely, the interaction with other co-occurring species has scarcely been addressed, despite the fact that the entire community may affect plant performance. We used woody vegetation patches as models to evaluate community facilitation in semi-arid steppes. We characterized biotic and physical attributes of 53 woody patches (patch size, litter accumulation, canopy density, vegetation cover, species number and identity, and phylogenetic distance), and soil fertility (organic C and total N), and evaluated their relative importance for the performance of seedlings of Pistacia lentiscus, a keystone woody species in western Mediterranean steppes. Seedlings were planted underneath the patches, and on their northern and southern edges. Woody patches positively affected seedling survival but not seedling growth. Soil fertility was higher underneath the patches than elsewhere. Physical and biotic attributes of woody patches affected seedling survival, but these effects depended on microsite conditions. The composition of the community of small shrubs and perennial grasses growing underneath the patches controlled seedling performance. An increase in Stipa tenacissima and a decrease in Brachypodium retusum increased the probability of survival. The cover of these species and other small shrubs, litter depth and community phylogenetic distance, were also related to seedling survival. Seedlings planted on the northern edge of the patches were mostly affected by attributes of the biotic community. These traits were of lesser importance in seedlings planted underneath and in the southern edge of patches, suggesting that constraints to seedling establishment differed within the patches. Our study highlights the importance of taking into consideration community attributes over pair-wise interactions when evaluating the outcome of ecological interactions in multi-specific communities, as they have profound implications in the composition, function and management of semi-arid steppes.

¿Qué caracteriza el conocimiento del profesor de matemáticas en la planificación del concepto de límite al infinito de una función para su enseñanza?

Se reportan avances de una investigación que se interesa por determinar las características del conocimiento matemático para la enseñanza del concepto de límite al infinito de una función que pone en acción el profesor en la planificación del tópico. El estudio se fundamenta en el modelo Conocimiento Matemático para la Enseñanza (MKT). En el estudio participan dos profesores de matemáticas de España y uno de México. Los datos se obtienen mediante una entrevista semiestructurada que involucró aspectos sobre los datos personales, el aula de clases, la planificación del profesor y del investigador sobre el tópico. El análisis de los daros se realiza en tres fases: generación de las unidades de análisis, agrupamiento en categorías de dichas unidades y determinación de las características del conocimiento del profesor. Los resultados evidencian que el profesor pone en acción los subdominios del MKT cuando planifica la enseñanza del concepto de límite al infinito de una función.