A Reciprocity Theorem for Monomer-Dimer Coverings

The problem of counting monomer-dimer coverings of a lattice is a longstanding problem in statistical mechanics. It has only been exactly solved for the special case of dimer coverings in two dimensions. In earlier work, Stanley proved a reciprocity principle governing the number $N(m,n)$ of dimer coverings of an $m$ by $n$ rectangular grid (also known as perfect matchings), where $m$ is fixed and $n$ is allowed to vary. As reinterpreted by Propp, Stanley's result concerns the unique way of extending $N(m,n)$ to $n < 0$ so that the resulting bi-infinite sequence, $N(m,n)$ for $n \in {Z}$, satisfies a linear recurrence relation with constant coefficients. In particular, Stanley shows that $N(m,n)$ is always an integer satisfying the relation $N(m,-2-n) = \epsilon_{m,n}N(m,n)$ where $\epsilon_{m,n} = 1$ unless $m\equiv$ 2(mod 4) and $n$ is odd, in which case $\epsilon_{m,n} = -1$. Furthermore, Propp's method is applicable to higher-dimensional cases. This paper discusses similar investigations of the numbers $M(m,n)$, of monomer-dimer coverings, or equivalently (not necessarily perfect) matchings of an $m$ by $n$ rectangular grid. We show that for each fixed $m$ there is a unique way of extending $M(m,n)$ to $n < 0$ so that the resulting bi-infinite sequence, $M(m,n)$ for $n \in {Z}$, satisfies a linear recurrence relation with constant coefficients. We show that $M(m,n)$, a priori a rational number, is always an integer, using a generalization of the combinatorial model offered by Propp. Lastly, we give a new statement of reciprocity in terms of multivariate generating functions from which Stanley's result follows.Comment: 13 pages, 12 figures, to appear in the proceedings of the Discrete Models for Complex Systems (DMCS) 2003 conference. (v2 - some minor changes

Publisher's Note: Defect Influence on Heteroepitaxial 3C-SiC Young's Modulus [Electrochem. Solid-State Lett., 14, H161 (2011)]

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Prompt electrons driving ion acceleration and formation of a two temperatures plasma in nanosecond laser-ablation domain

We present the results of an experiment on plasma generation via laser ablation at 10^12 W/cm^2 of power intensity and in a nanosecond domain. Prompt electrons emission and complex plasma plume fragmentation were simultaneously observed for the first time in this laser intensity regime, along with a double electron temperature inside the plasma bulk surviving for a long time to the plume expansion. 1D PIC simulations are in agreement with experimental data as long as the emission of initial prompt electrons is considered. This assumption results to be the key to explain all the other experimental evidences.Comment: 5 pages, 6 figures, Europhysics Letters in pres

Follow-Up of Coiled Cerebral Aneurysms at 3T: Comparison of 3D Time-of-Flight MR Angiography and Contrast-Enhanced MR Angiography

BACKGROUND AND PURPOSE: Our aim was to compare contrast-enhanced MR angiography (CE-MRA) and 3D time-of-flight (TOF) MRA at 3T for follow-up of coiled cerebral aneurysms. MATERIALS AND METHODS: Fifty-two patients treated with Guglielmi detachable coils for 54 cerebral aneurysms were evaluated at 3T MRA. 3D TOF MRA (TR/TE = 23/3.5; SENSE factor = 2.5) and CE-MRA by using a 3D ultrafast gradient-echo sequence (TR/TE = 5.9/1.8; SENSE factor = 3) enhanced with 0.1-mmol/kg gadobenate dimeglumine were performed in the same session. Source images, 3D maximum intensity projection, 3D shaded surface display, and/or 3D volume-rendered reconstructions were evaluated in terms of aneurysm occlusion/patency and artifact presence. RESULTS: In terms of clinical classification, the 2 MRA sequences were equivalent for 53 of the 54 treated aneurysms: 21 were considered fully occluded, whereas 16 were considered to have a residual neck and 16 were considered residually patent at follow-up MRA. The remaining aneurysm appeared fully occluded at TOF MRA but had a residual patent neck at CE-MRA. Visualization of residual aneurysm patency was significantly ( P = .001) better with CE-MRA compared with TOF MRA for 10 (31.3%) of the 32 treated aneurysms considered residually patent with both sequences. Coil artifacts were present in 5 cases at TOF MRA but in none at CE-MRA. No relationship was apparent between the visualization of patency and either the size of the aneurysm or the interval between embolization and follow-up. CONCLUSION: At follow-up MRA at 3T, unenhanced TOF and CE-MRA sequences are similarly effective at classifying coiled aneurysms as occluded or residually patent. However, CE-MRA is superior to TOF MRA for visualization of residual patency and is associated with fewer artifacts

IL-17 and its role in inflammatory, autoimmune, and oncological skin diseases. State of art

Recent data support the theory of the involvement of IL-17 in the pathogenesis of several chronic inflammatory skin diseases (psoriasis, atopic dermatitis, acne, hidradenitis suppurativa) and autoimmune skin diseases (alopecia areata, vitiligo, bullous diseases). Even if the role of IL-17 in inflammatory and autoimmune diseases has been reported extensively, its role in tumor is still controversial. Some reports show that Th17 cells eradicate tumors, while others reveal that they promote the initiation and early growth of tumors. Herein, we review the role of IL-17 in the involvement of some common dermatologic diseases: psoriasis, atopic dermatitis, hidradenitis suppurativa, acne, vitiligo, melanoma, and nonmelanoma skin cancers

Therapeutic options for the treatment of actinic keratosis with scalp and face localization

Actinic keratosis (AK) is a common skin disease related to ultraviolet chronic exposure, that is now considered a squamous cell carcinoma in situ. Primary skin cancer prevention strategies should be recommended for high risk patients. There is a wide spectrum of treatment options available for AKs, and several variables should be taken into account regarding the best therapeutic choice for each patient. The purpose of this article is to review the current treatment strategies for AKs localized on the face and scalp, with a focus on the practical point of view that could be useful for choosing the best therapeutic option. The two main therapeutic approaches will be distinguished first: lesion-directed and field-directed. Afterwards, the treatment based on clinical type and patient comorbidity will be discusse

A case of proliferative nodule arising within blue nevus

Blue nevi are a heterogeneous group of lesions that can display a variety of different clinicopathological characteristics. Although attempts are made to classify each lesion into defined subtypes, there can be overlap between the subtypes. The clinical, dermoscopic and histolopathologic features of a case of proliferative nodule arising within blue nevus is discussed. Running title: Blue nevi are an heterogeneous group of melanocytic lesions blue tinctorial properties. Proliferative nodules are rare benign lesions often present at birth as a component of a large congenital melanocytic nevi, congenital or acquired nevi. We first report a case of proliferative nodule arising within blue nevus

Substantia Nigra Volumetry with 3-T MRI in De Novo and Advanced Parkinson Disease

Background: Magnetization transfer–prepared T1-weighted MRI can depict a hyperintense subregion of the substantia nigra involved in the degeneration process of Parkinson disease. / Purpose: To evaluate quantitative measurement of substantia nigra volume by using MRI to support clinical diagnosis and staging of Parkinson disease. / Materials and Methods: In this prospective study, a high-spatial-resolution magnetization transfer–prepared T1-weighted volumetric sequence was performed with a 3-T MRI machine between January 2014 and October 2015 for participants with de novo Parkinson disease, advanced Parkinson disease, and healthy control participants. A reproducible semiautomatic quantification analysis method that entailed mesencephalic intensity as an internal reference was used for hyperintense substantia nigra volumetry normalized to intracranial volume. A general linear model with age and sex as covariates was used to compare the three groups. / Results: Eighty participants were evaluated: 20 healthy control participants (mean age ± standard deviation, 56 years ± 11; 11 women), 29 participants with de novo Parkinson disease (64 years ± 10; 19 men), and 31 participants with advanced Parkinson disease (60 years ± 9; 16 women). Volumetric measurement of hyperintense substantia nigra from magnetization transfer–prepared T1-weighted MRI helped differentiate healthy control participants from participants with advanced Parkinson disease (mean difference for ipsilateral side, 64 mm3 ± 14, P < .001; mean difference for contralateral side, 109 mm3 ± 14, P < .001) and helped distinguish healthy control participants from participants with de novo Parkinson disease (mean difference for ipsilateral side, 45 mm3 ± 15, P < .01; mean difference for contralateral side, 66 mm3 ± 15, P < .001) and participants with de novo Parkinson disease from those with advanced Parkinson disease (mean difference for ipsilateral side, 20 mm3 ± 13, P = .40; mean difference for contralateral side, 43 mm3 ± 13, P = .004). / Conclusion: Magnetization transfer–prepared T1-weighted MRI volumetry of the substantia nigra helped differentiate the stages of Parkinson disease

Unsuspected Involvement of Spinal Cord in Alzheimer Disease

OBJECTIVE: Brain atrophy is an established biomarker for dementia, yet spinal cord involvement has not been investigated to date. As the spinal cord is relaying sensorimotor control signals from the cortex to the peripheral nervous system and vice-versa, it is indeed a very interesting question to assess whether it is affected by atrophy due to a disease that is known for its involvement of cognitive domains first and foremost, with motor symptoms being clinically assessed too. We, therefore, hypothesize that in Alzheimer’s disease (AD), severe atrophy can affect the spinal cord too and that spinal cord atrophy is indeed an important in vivo imaging biomarker contributing to understanding neurodegeneration associated with dementia. METHODS: 3DT1 images of 31 AD and 35 healthy control (HC) subjects were processed to calculate volume of brain structures and cross-sectional area (CSA) and volume (CSV) of the cervical cord [per vertebra as well as the C2-C3 pair (CSA23 and CSV23)]. Correlated features (ρ > 0.7) were removed, and the best subset identified for patients’ classification with the Random Forest algorithm. General linear model regression was used to find significant differences between groups (p ≤ 0.05). Linear regression was implemented to assess the explained variance of the Mini-Mental State Examination (MMSE) score as a dependent variable with the best features as predictors. RESULTS: Spinal cord features were significantly reduced in AD, independently of brain volumes. Patients classification reached 76% accuracy when including CSA23 together with volumes of hippocampi, left amygdala, white and gray matter, with 74% sensitivity and 78% specificity. CSA23 alone explained 13% of MMSE variance. DISCUSSION: Our findings reveal that C2-C3 spinal cord atrophy contributes to discriminate AD from HC, together with more established features. The results show that CSA23, calculated from the same 3DT1 scan as all other brain volumes (including right and left hippocampi), has a considerable weight in classification tasks warranting further investigations. Together with recent studies revealing that AD atrophy is spread beyond the temporal lobes, our result adds the spinal cord to a number of unsuspected regions involved in the disease. Interestingly, spinal cord atrophy explains also cognitive scores, which could significantly impact how we model sensorimotor control in degenerative diseases with a primary cognitive domain involvement. Prospective studies should be purposely designed to understand the mechanisms of atrophy and the role of the spinal cord in AD