A new approach to local hardness

The applicability of the local hardness as defined by the derivative of the chemical potential with respect to the electron density is undermined by an essential ambiguity arising from this definition. Further, the local quantity defined in this way does not integrate to the (global) hardness - in contrast with the local softness, which integrates to the softness. It has also been shown recently that with the conventional formulae, the largest values of local hardness do not necessarily correspond to the hardest regions of a molecule. Here, in an attempt to fix these drawbacks, we propose a new approach to define and evaluate the local hardness. We define a local chemical potential, utilizing the fact that the chemical potential emerges as the additive constant term in the number-conserving functional derivative of the energy density functional. Then, differentiation of this local chemical potential with respect to the number of electrons leads to a local hardness that integrates to the hardness, and possesses a favourable property; namely, within any given electron system, it is in a local inverse relation with the Fukui function, which is known to be a proper indicator of local softness in the case of soft systems. Numerical tests for a few selected molecules and a detailed analysis, comparing the new definition of local hardness with the previous ones, show promising results.Comment: 30 pages (including 6 figures, 1 table

Needle-related ultrasound artifacts and their importance in anaesthetic practice

L

Neural basis of identity information extraction from noisy face images

Previous research has made significant progress in identifying the neural basis of the remarkably efficient and seemingly effortless face perception in humans. However, the neural processes that enable the extraction of facial information under challenging conditions when face images are noisy and deteriorated remains poorly understood. Here we investigated the neural processes underlying the extraction of identity information from noisy face images using fMRI. For each participant, we measured (1) face-identity discrimination performance outside the scanner, (2) visual cortical fMRI responses for intact and phase-randomized face stimuli, and (3) intrinsic functional connectivity using resting-state fMRI. Our whole-brain analysis showed that the presence of noise led to reduced and increased fMRI responses in the mid-fusiform gyrus and the lateral occipital cortex, respectively. Furthermore, the noise-induced modulation of the fMRI responses in the right face-selective fusiform face area (FFA) was closely associated with individual differences in the identity discrimination performance of noisy faces: smaller decrease of the fMRI responses was accompanied by better identity discrimination. The results also revealed that the strength of the intrinsic functional connectivity within the visual cortical network composed of bilateral FFA and bilateral object-selective lateral occipital cortex (LOC) predicted the participants' ability to discriminate the identity of noisy face images. These results imply that perception of facial identity in the case of noisy face images is subserved by neural computations within the right FFA as well as a re-entrant processing loop involving bilateral FFA and LOC. © 2015 the authors

Histological Study of the First Seven Days of Skin Wound Healing in Rats

The aim of this study was to elaborate a histological model of incisional skin wound healing in Sprague-Dawley rats. Under aseptic conditions two paravertebral full thickness skin incisions were performed on the back of 42 anesthetized male rats. Histological sections from tissue specimens were stained by hematoxylin and eosin, van Gieson, PAS + PSD, Mallory's phosphotungstic hematoxylin and azur and eosin and evaluated during the first seven days after surgery. Histological evaluation revealed that the regeneration of injured epidermis was completed five days after surgery. The inflammatory phase was recorded during the first three days of healing with the culmination of this phase between day one and day two. The beginning of the proliferative phase was dated to the first day and the peak during day five and day six. The initiation of the maturation and remodeling phase of the healing process was observed six days after wounding. At the layer of striated muscle, the centronucleated cells were described for the first time six days after surgery. The wound healing process of rat skin was histologically described during the first seven days. Results of this work can serve as an experimental model for further research using external pharmacological and physical factors (laser light, magnetic field) by which the wound healing can be favourably influenced

Domination of the rectangular queen's graph

The queen's graph $Q_{m \times n}$ has the squares of the $m \times n$ chessboard as its vertices; two squares are adjacent if they are in the same row, column, or diagonal of the board. A set $D$ of squares of $Q_{m \times n}$ is a dominating set for $Q_{m \times n}$ if every square of $Q_{m \times n}$ is either in $D$ or adjacent to a square in $D$. The minimum size of a dominating set of $Q_{m \times n}$ is the domination number, denoted by $\gamma(Q_{m \times n})$. Values of $\gamma(Q_{m \times n}), \, 4 \leq m \leq n \leq 18, \,$ are given here, in each case with a file of minimum dominating sets (often all of them, up to symmetry) in an online appendix at https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i4p45/HTML. In these ranges for $m$ and $n$, monotonicity fails once: $\gamma(Q_{8 \times 11}) = 6 > 5 = \gamma(Q_{9 \times 11}) = \gamma(Q_{10 \times 11}) = \gamma(Q_{11 \times 11})$. Lower bounds on $\gamma(Q_{m \times n})$ are given. In particular, if $m \leq n$ then $\gamma(Q_{m \times n}) \geq \min \{ m, \lceil (m+n-2)/4 \rceil \}$. A set of squares is independent if no two of its squares are adjacent. The minimum size of an independent dominating set of $Q_{m \times n}$ is the independent domination number, denoted by $i(Q_{m \times n})$. Values of $i(Q_{m \times n}), \, 4 \leq m \leq n \leq 18, \,$ are given here, in each case with some minimum dominating sets. In these ranges for $m$ and $n$, monotonicity fails twice: $i(Q_{8 \times 11}) = 6 > 5 = i(Q_{9 \times 11}) = i(Q_{10 \times 11}) = i(Q_{11 \times 11})$, and $i(Q_{11 \times 18}) = 9 > 8 = i(Q_{12 \times 18})$

On the Communication Complexity of Secure Computation

Information theoretically secure multi-party computation (MPC) is a central primitive of modern cryptography. However, relatively little is known about the communication complexity of this primitive. In this work, we develop powerful information theoretic tools to prove lower bounds on the communication complexity of MPC. We restrict ourselves to a 3-party setting in order to bring out the power of these tools without introducing too many complications. Our techniques include the use of a data processing inequality for residual information - i.e., the gap between mutual information and G\'acs-K\"orner common information, a new information inequality for 3-party protocols, and the idea of distribution switching by which lower bounds computed under certain worst-case scenarios can be shown to apply for the general case. Using these techniques we obtain tight bounds on communication complexity by MPC protocols for various interesting functions. In particular, we show concrete functions that have "communication-ideal" protocols, which achieve the minimum communication simultaneously on all links in the network. Also, we obtain the first explicit example of a function that incurs a higher communication cost than the input length in the secure computation model of Feige, Kilian and Naor (1994), who had shown that such functions exist. We also show that our communication bounds imply tight lower bounds on the amount of randomness required by MPC protocols for many interesting functions.Comment: 37 page