n-Ary quasigroups of order 4

We characterize the set of all N-ary quasigroups of order 4: every N-ary quasigroup of order 4 is permutably reducible or semilinear. Permutable reducibility means that an N-ary quasigroup can be represented as a composition of K-ary and (N-K+1)-ary quasigroups for some K from 2 to N-1, where the order of arguments in the representation can differ from the original order. The set of semilinear N-ary quasigroups has a characterization in terms of Boolean functions. Keywords: Latin hypercube, n-ary quasigroup, reducibilityComment: 10pp. V2: revise

Asymptotics for the number of n-quasigroups of order 4

The asymptotic form of the number of n-quasigroups of order 4 is $3^{n+1} 2^{2^n +1} (1+o(1))$. Keywords: n-quasigroups, MDS codes, decomposability, reducibility.Comment: 15 p., 3 fi

On the structure of non-full-rank perfect codes

The Krotov combining construction of perfect 1-error-correcting binary codes from 2000 and a theorem of Heden saying that every non-full-rank perfect 1-error-correcting binary code can be constructed by this combining construction is generalized to the $q$-ary case. Simply, every non-full-rank perfect code $C$ is the union of a well-defined family of $\mu$-components $K_\mu$, where $\mu$ belongs to an "outer" perfect code $C^*$, and these components are at distance three from each other. Components from distinct codes can thus freely be combined to obtain new perfect codes. The Phelps general product construction of perfect binary code from 1984 is generalized to obtain $\mu$-components, and new lower bounds on the number of perfect 1-error-correcting $q$-ary codes are presented.Comment: 8 page

Changes of some blood indices and myocardial electrolyte content during hypokinesia

Using special hypokinetic cages, the volume changes of circulating blood, its hematocrit and protein content, volume ratios between extra- and intracellular liquids in the body, as well as electrolyte content in the blood and myocardium during hypokinesia were investigated experimentally in rabbits

An upper bound on the number of frequency hypercubes

A frequency $n$-cube $F^n(q;l_0,...,l_{m-1})$ is an $n$-dimensional $q$-by-...-by-$q$ array, where $q = l_0+...+l_{m-1}$, filled by numbers $0,...,m-1$ with the property that each line contains exactly $l_i$ cells with symbol $i$, $i = 0,...,m-1$ (a line consists of $q$ cells of the array differing in one coordinate). The trivial upper bound on the number of frequency $n$-cubes is $m^{(q-1)^{n}}$. We improve that lower bound for $n>2$, replacing $q-1$ by a smaller value, by constructing a testing set of size $s^{n}$, $s<q-1$, for frequency $n$-cubes (a testing sets is a collection of cells of an array the values in which uniquely determine the array with given parameters). We also construct new testing sets for generalized frequency $n$-cubes, which are essentially correlation-immune functions in $n$ $q$-valued arguments; the cardinalities of new testing sets are smaller than for testing sets known before. Keywords: frequency hypercube, correlation-immune function, latin hypercube, testing set

Experimental investigation of the role of thyrocalcitonin in the prophylaxis of disturbances in the water-salt and mineral metabolism during a 30-day hypokinesia

The effect of thyrocalcitonin (TCT) injections on the metabolism of water and electrolytes in free-moving and immobilized chinchilla hares is described. Calcium excretion from immobilized animals was elevated, but normalized in those also receiving TCT injections. TCT also normalized water content and excretion rates

Optimized Model of Cerebral Ischemia In situ for the Long-Lasting Assessment of Hippocampal Cell Death

Among all the brain, the hippocampus is the most susceptible region to ischemic lesion, with the highest vulnerability of CA1 pyramidal neurons to ischemic damage. This damage may cause either prompt neuronal death (within hours) or with a delayed appearance (over days), providing a window for applying potential therapies to reduce or prevent ischemic impairments. However, the time course when ischemic damage turns to neuronal death strictly depends on experimental modeling of cerebral ischemia and, up to now, studies were predominantly focused on a short time-window—from hours to up to a few days post-lesion. Using different schemes of oxygen-glucose deprivation (OGD), the conditions taking place upon cerebral ischemia, we optimized a model of mimicking ischemic conditions in organotypical hippocampal slices for the long-lasting assessment of CA1 neuronal death (at least 3 weeks). By combining morphology and electrophysiology, we show that prolonged (30-min duration) OGD results in a massive neuronal death and overwhelmed astrogliosis within a week post-OGD whereas OGD of a shorter duration (10-min) triggered programmed CA1 neuronal death with a significant delay—within 2 weeks—accompanied with drastically impaired CA1 neuron functions. Our results provide a rationale toward optimized modeling of cerebral ischemia for reliable examination of potential treatments for brain neuroprotection, neuro-regeneration, or testing neuroprotective compounds in situ

On Pure Spinor Superfield Formalism

We show that a certain superfield formalism can be used to find an off-shell supersymmetric description for some supersymmetric field theories where conventional superfield formalism does not work. This "new" formalism contains even auxiliary variables in addition to conventional odd super-coordinates. The idea of this construction is similar to the pure spinor formalism developed by N.Berkovits. It is demonstrated that using this formalism it is possible to prove that the certain Chern-Simons-like (Witten's OSFT-like) theory can be considered as an off-shell version for some on-shell supersymmetric field theories. We use the simplest non-trivial model found in [2] to illustrate the power of this pure spinor superfield formalism. Then we redo all the calculations for the case of 10-dimensional Super-Yang-Mills theory. The construction of off-shell description for this theory is more subtle in comparison with the model of [2] and requires additional Z_2 projection. We discover experimentally (through a direct explicit calculation) a non-trivial Z_2 duality at the level of Feynman diagrams. The nature of this duality requires a better investigation

Mechanisms of water-salt metabolism disturbances in dogs subjected to six month hypokinesia

Water-salt metabolism in dogs during prolonged restricted motor activity (hypokinesia) was investigated. It was found that hydration occurred and fluid was redistributed between the extra- and intra-cellular sectors. Also, electrolyte excretion rose, and magnetism and calcium metabolism changed significantly. It is concluded that the forces caused by muscle strain proper (which was decreased under conditions of hypokinesia) influence the state of bone metabolism

Opposite, bidirectional shifts in excitation and inhibition in specific types of dorsal horn interneurons are associated with spasticity and pain post-SCI

Spasticity, a common complication after spinal cord injury (SCI), is frequently accompanied by chronic pain. The physiological origin of this pain (critical to its treatment) remains unknown, although spastic motor dysfunction has been related to the hyperexcitability of motoneurons and to changes in spinal sensory processing. Here we show that the pain mechanism involves changes in sensory circuits of the dorsal horn (DH) where nociceptive inputs integrate for pain processing. Spasticity is associated with the DH hyperexcitability resulting from an increase in excitation and disinhibition occurring in two respective types of sensory interneurons. In the tonic-firing inhibitory lamina II interneurons, glutamatergic drive was reduced while glycinergic inhibition was potentiated. In contrast, excitatory drive was boosted to the adapting-firing excitatory lamina II interneurons while GABAergic and glycinergic inhibition were reduced. Thus, increased activity of excitatory DH interneurons coupled with the reduced excitability of inhibitory DH interneurons post-SCI could provide a neurophysiological mechanism of central sensitization and chronic pain associated with spasticity