Fidelity and Concurrence of conjugated states

We prove some new properties of fidelity (transition probability) and concurrence, the latter defined by straightforward extension of Wootters notation. Choose a conjugation and consider the dependence of fidelity or of concurrence on conjugated pairs of density operators. These functions turn out to be concave or convex roofs. Optimal decompositions are constructed. Some applications to two- and tripartite systems illustrate the general theorem.Comment: 10 pages, RevTex, Correction: Enlarged, reorganized version. More explanation

SBV regularity for Hamilton-Jacobi equations in Rn\mathbb R^n

In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$\partial_t u + H(D_{x} u)=0 \qquad \textrm{in} \Omega\subset \mathbb R\times \mathbb R^{n} .$$ In particular, under the assumption that the Hamiltonian $H\in C^2(\mathbb R^n)$ is uniformly convex, we prove that $D_{x}u$ and $\partial_t u$ belong to the class $SBV_{loc}(\Omega)$.Comment: 15 page

Cathode Active Material Recycling from Spent Lithium Batteries: A Green (Circular) Approach Based on Deep Eutectic Solvents

The transition to a circular economy vision must handle the increasing request of metals required to satisfy the battery industry; this can be obtained by recycling and feeding back secondary raw materials recovered through proper waste management. Here, a novel and green proof-of-concept was developed, based on deep eutectic solvents (DESs) to fully and easily recover valuable metals from various cathode active materials, including LiMn2O4, LiNi0.5Mn1.5O4, and LiNi0.8Co0.2O2. DES composed of choline chloride and lactic acid could leach Li, Mn, Co, and Ni, achieving efficiency of 100 % under much milder conditions with respect to the previous literature. For the first time, to our best knowledge, a two-step approach was reported in the case of LiNi0.8Co0.2O2 for selective recovery of Li, Co, and Ni with high yield and purity. Furthermore, other cathode components, namely aluminum current collector and binder, were found to be not dissolved by the proposed DES, thus making a simple separation from the active material possible. Finally, this strategy was designed to easily regenerate and reuse the leaching solvents for more than one extraction, thus further boosting process sustainability

Convergence of Ginzburg-Landau functionals in 3-d superconductivity

In this paper we consider the asymptotic behavior of the Ginzburg- Landau model for superconductivity in 3-d, in various energy regimes. We rigorously derive, through an analysis via {\Gamma}-convergence, a reduced model for the vortex density, and we deduce a curvature equation for the vortex lines. In a companion paper, we describe further applications to superconductivity and superfluidity, such as general expressions for the first critical magnetic field H_{c1}, and the critical angular velocity of rotating Bose-Einstein condensates.Comment: 45 page

Two patients with history of STEC-HUS, posttransplant recurrence and complement gene mutations

Hemolytic uremic syndrome (HUS) is a disease of microangiopathic hemolytic anemia, thrombocytopenia and acute renal failure. About 90% of cases are secondary to infections by Escherichia coli strains producing Shiga-like toxins (STEC-HUS), while 10% are associated with mutations in genes encoding proteins of complement system (aHUS). We describe two patients with a clinical history of STEC-HUS, who developed end-stage renal disease (ESRD) soon after disease onset. They received a kidney transplant but lost the graft for HUS recurrence, a complication more commonly observed in aHUS. Before planning a second renal transplantation, the two patients underwent genetic screening for aHUS-associated mutations that revealed the presence of a heterozygous CFI mutation in patient #1 and a heterozygous MCP mutation in patient #2, and also in her mother who donated the kidney. This finding argues that the two cases originally diagnosed as STEC-HUS had indeed aHUS triggered by STEC infection on a genetic background of impaired complement regulation. Complement gene sequencing should be performed before kidney transplantation in patients who developed ESRD following STEC-HUS since they may be undiagnosed cases of aHUS, at risk of posttransplant recurrence. Furthermore, genetic analysis of donors is mandatory before living-related transplantation to exclude carriers of HUS-predisposing mutations. Two patients with a clinical history of D+ hemolytic uremic syndrome associated with Shiga-toxin-producing 0157:H7 E. coli and recurrence in the kidney graft carry heterozygous mutations in the genes encoding complement factor I (patient 1) and membrane cofactor protein (patient 2). © Copyright 2013 The American Society of Transplantation and the American Society of Transplant Surgeons

On quantum coding for ensembles of mixed states

We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of compression of mixed states. We also discuss a classical analogue of the problem.Comment: 23 pages, LaTe

Striped periodic minimizers of a two-dimensional model for martensitic phase transitions

In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Mueller, is defined by the following functional: $${\cal E}(u)=\beta||u(0,\cdot)||^2_{H^{1/2}([0,h])}+ \int_{0}^{L} dx \int_0^h dy \big(|u_x|^2 + \epsilon |u_{yy}| \big)$$ where $u:[0,L]\times[0,h]\to R$ is periodic in $y$ and $u_y=\pm 1$ almost everywhere. Conti proved that if $\beta\gtrsim\epsilon L/h^2$ then the minimal specific energy scales like $\sim \min\{(\epsilon\beta/L)^{1/2}, (\epsilon/L)^{2/3}\}$, as $(\epsilon/L)\to 0$. In the regime $(\epsilon\beta/L)^{1/2}\ll (\epsilon/L)^{2/3}$, we improve Conti's results, by computing exactly the minimal energy and by proving that minimizers are periodic one-dimensional sawtooth functions.Comment: 29 pages, 3 figure

Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes

The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results which have been obtained, both in two and higher dimensions. In particular, we describe how the phenomenological Wulff and Winterbottom constructions can be derived from the microscopic description provided by the equilibrium statistical mechanics of lattice gases. We focus on the main conceptual issues and describe the central ideas of the existing approaches.Comment: To appear in the March 2000 special issue of Journal of Mathematical Physics on Probabilistic Methods in Statistical Physic

Wharton’s Jelly Mesenchymal Stromal Cells Support the Expansion of Cord Blood–derived CD34 + Cells Mimicking a Hematopoietic Niche in a Direct Cell–cell Contact Culture System

Wharton’s jelly mesenchymal stromal cells (WJ-MSCs) have been recently exploited as a feeder layer in coculture systems to expand umbilical cord blood–hematopoietic stem/progenitor cells (UCB-HSPCs). Here, we investigated the role of WJ-MSCs in supporting ex vivo UCB-HSPC expansion either when cultured in direct contact (DC) with WJ-MSCs or separated by a transwell system or in the presence of WJ-MSC–conditioned medium. We found, in short-term culture, a greater degree of expansion of UCB-CD34 + cells in a DC system (15.7 ± 4.1-fold increase) with respect to the other conditions. Moreover, in DC, we evidenced two different CD34 + cell populations (one floating and one adherent to WJ-MSCs) with different phenotypic and functional characteristics. Both multipotent CD34 + /CD38 − and lineage-committed CD34 + /CD38 + hematopoietic progenitors were expanded in a DC system. The former were significantly more represented in the adherent cell fraction than in the floating one (18.7 ± 11.2% vs. 9.7 ± 7.9% over the total CD34 + cells). Short-term colony forming unit (CFU) assays showed that HSPCs adherent to the stromal layer were able to generate a higher frequency of immature colonies (CFU-granulocyte/macrophage and burst-forming unit erythroid/large colonies) with respect to the floating cells. In the attempt to identify molecules that may play a role in supporting the observed ex vivo HSPC growth, we performed secretome analyses. We found a number of proteins involved in the HSPC homing, self-renewal, and differentiation in all tested conditions. It is important to note that a set of sixteen proteins, which are only in part reported to be expressed in any hematopoietic niche, were exclusively found in the DC system secretome. In conclusion, WJ-MSCs allowed a significant ex vivo expansion of multipotent as well as committed HSPCs. This may be relevant for future clinical applications