Some Nearly Quantum Theories

We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras. Subject to some reasonable constraints, we show that no such composite exists having the exceptional Jordan algebra as a direct summand. We then construct several dagger compact categories of such Jordan-algebraic models. One of these neatly unifies real, complex and quaternionic mixed-state quantum mechanics, with the exception of the quaternionic "bit". Another is similar, except in that (i) it excludes the quaternionic bit, and (ii) the composite of two complex quantum systems comes with an extra classical bit. In both of these categories, states are morphisms from systems to the tensor unit, which helps give the categorical structure a clear operational interpretation. A no-go result shows that the first of these categories, at least, cannot be extended to include spin factors other than the (real, complex, and quaternionic) quantum bits, while preserving the representation of states as morphisms. The same is true for attempts to extend the second category to even-dimensional spin-factors. Interesting phenomena exhibited by some composites in these categories include failure of local tomography, supermultiplicativity of the maximal number of mutually distinguishable states, and mixed states whose marginals are pure.Comment: In Proceedings QPL 2015, arXiv:1511.0118

Composites and Categories of Euclidean Jordan Algebras

We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras (EJAs), satisfying some reasonable additional constraints motivated by the desire to construct dagger-compact categories of such models. We show that no such composite has the exceptional Jordan algebra as a direct summand, nor does any such composite exist if one factor has an exceptional summand, unless the other factor is a direct sum of one-dimensional Jordan algebras (representing essentially a classical system). Moreover, we show that any composite of simple, non-exceptional EJAs is a direct summand of their universal tensor product, sharply limiting the possibilities. These results warrant our focussing on concrete Jordan algebras of hermitian matrices, i.e., euclidean Jordan algebras with a preferred embedding in a complex matrix algebra}. We show that these can be organized in a natural way as a symmetric monoidal category, albeit one that is not compact closed. We then construct a related category InvQM of embedded euclidean Jordan algebras, having fewer objects but more morphisms, that is not only compact closed but dagger-compact. This category unifies finite-dimensional real, complex and quaternionic mixed-state quantum mechanics, except that the composite of two complex quantum systems comes with an extra classical bit. Our notion of composite requires neither tomographic locality, nor preservation of purity under tensor product. The categories we construct include examples in which both of these conditions fail. In such cases, the information capacity (the maximum number of mutually distinguishable states) of a composite is greater than the product of the capacities of its constituents.Comment: 60 pages, 3 tables. Substantially revised, with some new result

Newly-Discovered Planets Orbiting HD~5319, HD~11506, HD~75784 and HD~10442 from the N2K Consortium

Initially designed to discover short-period planets, the N2K campaign has since evolved to discover new worlds at large separations from their host stars. Detecting such worlds will help determine the giant planet occurrence at semi-major axes beyond the ice line, where gas giants are thought to mostly form. Here we report four newly-discovered gas giant planets (with minimum masses ranging from 0.4 to 2.1 MJup) orbiting stars monitored as part of the N2K program. Two of these planets orbit stars already known to host planets: HD 5319 and HD 11506. The remaining discoveries reside in previously-unknown planetary systems: HD 10442 and HD 75784. The refined orbital period of the inner planet orbiting HD 5319 is 641 days. The newly-discovered outer planet orbits in 886 days. The large masses combined with the proximity to a 4:3 mean motion resonance make this system a challenge to explain with current formation and migration theories. HD 11506 has one confirmed planet, and here we confirm a second. The outer planet has an orbital period of 1627.5 days, and the newly-discovered inner planet orbits in 223.6 days. A planet has also been discovered orbiting HD 75784 with an orbital period of 341.7 days. There is evidence for a longer period signal; however, several more years of observations are needed to put tight constraints on the Keplerian parameters for the outer planet. Lastly, an additional planet has been detected orbiting HD 10442 with a period of 1043 days.Comment: Accepted for publication in Ap

Value Encoding in Single Neurons in the Human Amygdala during Decision Making

A growing consensus suggests that the brain makes simple choices by assigning values to the stimuli under consideration and then comparing these values to make a decision. However, the network involved in computing the values has not yet been fully characterized. Here, we investigated whether the human amygdala plays a role in the computation of stimulus values at the time of decision making. We recorded single neuron activity from the amygdala of awake patients while they made simple purchase decisions over food items. We found 16 amygdala neurons, located primarily in the basolateral nucleus that responded linearly to the values assigned to individual items

Topological Signals of Singularities in Ricci Flow

We implement methods from computational homology to obtain a topological signal of singularity formation in a selection of geometries evolved numerically by Ricci flow. Our approach, based on persistent homology, produces precise, quantitative measures describing the behavior of an entire collection of data across a discrete sample of times. We analyze the topological signals of geometric criticality obtained numerically from the application of persistent homology to models manifesting singularities under Ricci flow. The results we obtain for these numerical models suggest that the topological signals distinguish global singularity formation (collapse to a round point) from local singularity formation (neckpinch). Finally, we discuss the interpretation and implication of these results and future applications.Comment: 24 pages, 14 figure

Hubble Space Telescope Imaging and Spectroscopy of the Sirius-Like Triple Star System HD 217411

We present Hubble Space Telescope imaging and spectroscopy of HD 217411, a G3 V star associated with the extreme ultraviolet excess source (EUV 2RE J2300-07.0). This star is revealed to be a triple system with a G 3V primary (HD 217411 A) separated by ~1.1" from a secondary that is in turn composed of an unresolved K0 V star (HD 217411 Ba) and a hot DA white dwarf (HD 217411 Bb). The hot white dwarf dominates the UV flux of the system. However; it is in turn dominated by the K0 V component beyond 3000 {\AA}. A revised distance of 143 pc is estimated for the system. A low level photometric modulation having a period of 0.61 days has also been observed in this system along with a rotational velocity on the order of 60 km s-1 in the K0 V star. Together both observations point to a possible wind induced spin up of the K0 V star during the AGB phase of the white dwarf. The nature of all three components is discussed as are constraints on the orbits, system age and evolution.Comment: 11 pages, 6 figure

Locally Tomographic Shadows (Extended Abstract)

Given a monoidal probabilistic theory -- a symmetric monoidal category $\mathcal{C}$ of systems and processes, together with a functor $\mathbf{V}$ assigning concrete probabilistic models to objects of $\mathcal{C}$ -- we construct a locally tomographic probabilistic theory LT$(\mathcal{C},\mathbf{V})$ -- the locally tomographic shadow of $(\mathcal{C},\mathbf{V})$ -- describing phenomena observable by local agents controlling systems in $\mathcal{C}$, and able to pool information about joint measurements made on those systems. Some globally distinct states become locally indistinguishable in LT$(\mathcal{C},\mathbf{V})$, and we restrict the set of processes to those that respect this indistinguishability. This construction is investigated in some detail for real quantum theory.Comment: In Proceedings QPL 2023, arXiv:2308.1548