Division, adjoints, and dualities of bilinear maps

The distributive property can be studied through bilinear maps and various morphisms between these maps. The adjoint-morphisms between bilinear maps establish a complete abelian category with projectives and admits a duality. Thus the adjoint category is not a module category but nevertheless it is suitably familiar. The universal properties have geometric perspectives. For example, products are orthogonal sums. The bilinear division maps are the simple bimaps with respect to nondegenerate adjoint-morphisms. That formalizes the understanding that the atoms of linear geometries are algebraic objects with no zero-divisors. Adjoint-isomorphism coincides with principal isotopism; hence, nonassociative division rings can be studied within this framework. This also corrects an error in an earlier pre-print; see Remark 2.11

Donaldson-Thomas invariants and wall-crossing formulas

Notes from the report at the Fields institute in Toronto. We introduce the Donaldson-Thomas invariants and describe the wall-crossing formulas for numerical Donaldson-Thomas invariants.Comment: 18 pages. To appear in the Fields Institute Monograph Serie

Exciton spin dynamics and photoluminescence polarization of CdSe/CdS dot-in-rod nanocrystals in high magnetic fields

The exciton spin dynamics and polarization properties of the related emission are investigated in colloidal CdSe/CdS dot-in-rod (DiR) and spherical core/shell nanocrystal (NC) ensembles by magneto-optical photoluminescence (PL) spectroscopy in magnetic fields up to 15 T. It is shown that the degree of circular polarization (DCP) of the exciton emission induced by the magnetic field is affected by the NC geometry as well as the exciton fine structure and can provide information on nanorod orientation. A theory to describe the circular and linear polarization properties of the NC emission in magnetic field is developed. It takes into account phonon mediated coupling between the exciton fine structure states as well as the dielectric enhancement effect resulting from the anisotropic shell of DiR NCs. This theoretical approach is used to model the experimental results and allows us to explain most of the measured features. The spin dynamics of the dark excitons is investigated in magnetic fields by time-resolved photoluminescence. The results highlight the importance of confined acoustic phonons in the spin relaxation of dark excitons. The bare core surface as well as the core/shell interface give rise to an efficient spin relaxation channel, while the surface of core/shell NCs seems to play only a minor role.Comment: 18 pages, 15 figure

Towards Mixed Gr{\"o}bner Basis Algorithms: the Multihomogeneous and Sparse Case

One of the biggest open problems in computational algebra is the design of efficient algorithms for Gr{\"o}bner basis computations that take into account the sparsity of the input polynomials. We can perform such computations in the case of unmixed polynomial systems, that is systems with polynomials having the same support, using the approach of Faug{\`e}re, Spaenlehauer, and Svartz [ISSAC'14]. We present two algorithms for sparse Gr{\"o}bner bases computations for mixed systems. The first one computes with mixed sparse systems and exploits the supports of the polynomials. Under regularity assumptions, it performs no reductions to zero. For mixed, square, and 0-dimensional multihomogeneous polynomial systems, we present a dedicated, and potentially more efficient, algorithm that exploits different algebraic properties that performs no reduction to zero. We give an explicit bound for the maximal degree appearing in the computations

Coherent strong-field control of multiple states by a single chirped femtosecond laser pulse

We present a joint experimental and theoretical study on strong-field photo-ionization of sodium atoms using chirped femtosecond laser pulses. By tuning the chirp parameter, selectivity among the population in the highly excited states 5p, 6p, 7p and 5f, 6f is achieved. Different excitation pathways enabling control are identified by simultaneous ionization and measurement of photoelectron angular distributions employing the velocity map imaging technique. Free electron wave packets at an energy of around 1 eV are observed. These photoelectrons originate from two channels. The predominant 2+1+1 Resonance Enhanced Multi-Photon Ionization (REMPI) proceeds via the strongly driven two-photon transition $4s\leftarrow\leftarrow3s$, and subsequent ionization from the states 5p, 6p and 7p whereas the second pathway involves 3+1 REMPI via the states 5f and 6f. In addition, electron wave packets from two-photon ionization of the non-resonant transiently populated state 3p are observed close to the ionization threshold. A mainly qualitative five-state model for the predominant excitation channel is studied theoretically to provide insights into the physical mechanisms at play. Our analysis shows that by tuning the chirp parameter the dynamics is effectively controlled by dynamic Stark-shifts and level crossings. In particular, we show that under the experimental conditions the passage through an uncommon three-state "bow-tie" level crossing allows the preparation of coherent superposition states

Habitual Green Kiwifruit Consumption Is Associated with a Reduction in Upper Gastrointestinal Symptoms: A Systematic Scoping Review

Kiwifruit have known positive effects on digestion. During clinical intervention trials using kiwifruit to improve constipation, upper gastrointestinal (GI) symptoms such as abdominal discomfort and pain, indigestion, and reflux were also alleviated. We aimed to evaluate the evidence for upper GI symptom relief by kiwifruit in clinical trials on participants with functional constipation (FC), irritable bowel syndrome with constipation (IBS-C), and healthy participants, and to elucidate which symptoms may be relieved and whether a difference exists between the effects of gold and green kiwifruit. We executed a systematic scoping review of 3 electronic databases from 1947 through January 2021 to identify clinical trials that reported effects of green or gold kiwifruit or kiwifruit compounds on upper GI symptoms as secondary outcomes in healthy participants or participants with FC or IBS-C. Studies were divided into those using the Gastrointestinal Symptom Rating Scale (GSRS) and those using alternative measurement tools. GSRS outcomes were pooled and statistically analyzed; non-GSRS outcomes were summarized. We identified 12 clinical trials with a total of 661 participants (124 controls, 537 receiving intervention) providing evidence for symptom relief of upper GI symptoms by kiwifruit intake. Only 5 of the 12 clinical trials used the GSRS to assess upper GI symptom relief. We found good evidence that green kiwifruit may reduce abdominal discomfort and pain, and some evidence that kiwifruit consumption may attenuate indigestion. Pooled GSRS outcome analysis indicates an average reduction of -0.85 (95% CI: -1.1, -0.57; Z = 6.1) in abdominal pain scores and -0.33 (95% CI: -0.52, -0.15; Z = -3.5) in indigestion scores with habitual kiwifruit consumption. While the number of studies reporting on upper GI symptom relief with a comparable measurement is limited, there is consistent evidence for the efficacy of kiwifruit on upper GI symptom relief. More research to strengthen the evidence is recommended.Statement of Significance: This is the first review showing evidence that habitual consumption of kiwifruit may improve upper gastrointestinal symptoms such as abdominal pain and dyspepsia

Direct Observation of High-Spin States in Manganese Dimer and Trimer Cations by X-ray Magnetic Circular Dichroism Spectroscopy in an Ion Trap

The electronic structure and magnetic moments of free Mn$_2^+$ and Mn$_3^+$ are characterized by $2p$ x-ray absorption and x-ray magnetic circular dichroism spectroscopy in a cryogenic ion trap that is coupled to a synchrotron radiation beamline. Our results show directly that localized magnetic moments of 5 $\mu_B$ are created by $3d^5 (^6\mathrm{S})$ states at each ionic core, which are coupled in parallel to form molecular high-spin states via indirect exchange that is mediated in both cases by a delocalized valence electron in a singly-occupied $4s$ derived orbital with an unpaired spin. This leads to total magnetic moments of 11 $\mu_B$ for Mn$_2^+$ and 16 $\mu_B$ for Mn$_3^+$, with no contribution of orbital angular momentum

Affine and toric hyperplane arrangements

We extend the Billera-Ehrenborg-Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements. For arrangements on the torus, we also generalize Zaslavsky's fundamental results on the number of regions.Comment: 32 pages, 4 figure