Atypical functioning of female genitalia explains monandry in a butterfly

Monandrous species are rare in nature, especially in animals where males transfer nutrients to females in the ejaculate. The proximate mechanisms responsible for monandry are poorly studied. In butterflies and moths, the male transfers a nutritious spermatophore into the corpus bursae (CB) of the female. The CB is a multifunctional organ that digests the spermatophore and has partial control of the post-mating sexual receptivity of the female. The spermatophore distends the CB and the post-mating sexual receptivity of the female is inversely proportional to the degree of distension. The CB of many butterfly species has a muscular sheath whose contractions mechanically contribute to digest the spermatophore. As the contents of the CB are absorbed, the degree of distension decreases and the female recovers receptivity. We studied the monandrous butterfly Leptophobia aripa (Boisduval, 1836) (Pieridae) and found that females do not digest the spermatophores. We investigated the structure of the CB and found that a muscular sheath is absent, indicating that in this butterfly females lack the necessary “apparatus” for the mechanical digestion of the spermatophore. We propose that female monandry in this species is result of its incapability to mechanically digest the spermatophore, which results in a constant degree of CB distension after mating and, thus, in the maintenance of the sexually unreceptive state of females. Hypotheses on the evolution of this mechanism are discussed.

Lower Bounds on OBDD Proofs with Several Orders

This article is motivated by seeking lower bounds on OBDD(∧, w, r) refutations, namely, OBDD refutations that allow weakening and arbitrary reorderings. We first work with 1 - NBP ∧ refutations based on read-once nondeterministic branching programs. These generalize OBDD(∧, r) refutations. There are polynomial size 1 - NBP(∧) refutations of the pigeonhole principle, hence 1-NBP(∧) is strictly stronger than OBDD}(∧, r). There are also formulas that have polynomial size tree-like resolution refutations but require exponential size 1-NBP(∧) refutations. As a corollary, OBDD}(∧, r) does not simulate tree-like resolution, answering a previously open question. The system 1-NBP(∧, ∃) uses projection inferences instead of weakening. 1-NBP(∧, ∃ k is the system restricted to projection on at most k distinct variables. We construct explicit constant degree graphs G n on n vertices and an ε > 0, such that 1-NBP(∧, ∃ ε n ) refutations of the Tseitin formula for G n require exponential size. Second, we study the proof system OBDD}(∧, w, r ℓ ), which allows ℓ different variable orders in a refutation. We prove an exponential lower bound on the complexity of tree-like OBDD(∧, w, r ℓ ) refutations for ℓ = ε log n , where n is the number of variables and ε > 0 is a constant. The lower bound is based on multiparty communication complexity.

Rotating stealth black holes with a cohomogeneity$$-1$$ metric

In five dimensions we consider a general shift symmetric and parity preserving scalar tensor action that contains up to second order covariant derivatives of the scalar field. A rotating stealth black hole solution is constructed where the metric is given by the Myers–Perry spacetime with equal momenta and the scalar field is identified with the Hamilton–Jacobi potential. This nontrivial scalar field has an extra hair associated with the rest mass of the test particle, and the solution does not require any fine tuning of the coupling functions of the theory. Interestingly enough, we show that the disformal transformation, generated by this scalar field, and with a constant degree of disformality, leaves invariant (up to diffeomorphisms) the Myers–Perry metric with equal momenta. This means that the hair of the scalar field, along with the constant disformality parameter, can be consistently absorbed into further redefinitions of the mass and of the single angular parameter of the disformed metric. These results are extended in higher odd dimensions with a Myers–Perry metric for which all the momenta are equal. The key of the invariance under disformal transformation of the metric is mainly the cohomogeneity$$-1$$ - 1 character of the Myers–Perry metric with equal momenta. Starting from this observation, we consider a general class of cohomogeneity$$-1$$ - 1 metrics in arbitrary dimension, and we list the conditions ensuring that this class of metrics remain invariant (up to diffeomorphisms) under a disformal transformation with a constant degree of disformality and with a scalar field with constant kinetic term. The extension to the Kerr+-de Sitter case is also considered where it is shown that rotating stealth solutions may exist provided some fine tuning of the coupling functions of the scalar tensor theory.

Evolution of calcite microcrystal morphology during experimental dissolution

Phanerozoic limestones are composed of low-Mg calcite microcrystals (i.e., micrite) that typically measure between 1 and 9 μm in diameter. These microcrystals, which host most of the microporosity in subsurface reservoirs, are characterized by a variety of microtextures. Despite the overwhelming consensus that calcite microcrystals are diagenetic, the origin of the various textures is widely debated. The most commonly reported texture is characterized by polyhedral and rounded calcite microcrystals, which are interpreted to form via partial dissolution of rhombic microcrystals during burial diagenesis. A proposed implication of this model is that dissolution during burial is responsible for significant porosity generation. This claim has been previously criticized based on mass-balance considerations and geochemical constrains. To explicitly test the dissolution model, a series of laboratory experiments were conducted whereby various types of calcites composed of rhombic and polyhedral microcrystals were partially dissolved under a constant degree of undersaturation, both near and far-from-equilibrium. Our results indicate that calcite crystals dissolved under far-from-equilibrium conditions develop rounded edges and corners, inter-crystal gulfs (narrow grooves or channels between adjacent crystals), and a few etch pits on crystal faces—observations consistent with the burial-dissolution hypothesis. Crystals dissolved under near-equilibrium conditions, in contrast, retain sharp edges and corners and develop ledges and pits—suggesting that dissolution occurs more selectively at high-energy sites. These observations support the longstanding understanding that far-from-equilibrium dissolution is transport-controlled, and near-equilibrium dissolution is surface-controlled. Our results also show that while the rhombic calcite crystals may develop rounded edges and corners when dissolved under far-from-equilibrium conditions the crystals themselves do not become spherical. By contrast, polyhedral crystals not only develop rounded edges and corners when dissolved under far-from-equilibrium conditions but become nearly spherical with continued dissolution. Collectively, these observations suggest that rounded calcite microcrystals more likely form from a precursor exhibiting an equant polyhedral texture, rather than from a euhedral rhombic precursor as previously proposed. Lastly, the observation that calcite crystals developed rounded edges and corners and inter-crystal gulfs after only 5% dissolution indicates that the presence of such features in natural limestones need not imply that significant porosity generation has occurred.

Disforming the Kerr metric

Starting from a recently constructed stealth Kerr solution of higher order scalar tensor theory involving scalar hair, we analytically construct disformal versions of the Kerr spacetime with a constant degree of disformality and a regular scalar field. While the disformed metric has only a ring singularity and asymptotically is quite similar to Kerr, it is found to be neither Ricci flat nor circular. Non-circularity has far reaching consequences on the structure of the solution. As we approach the rotating compact object from asymptotic infinity we find a static limit ergosurface similar to the Kerr spacetime with an enclosed ergoregion. However, the stationary limit of infalling observers is found to be a timelike hypersurface. A candidate event horizon is found in the interior of this stationary limit surface. It is a null hypersurface generated by a null congruence of light rays which are no longer Killing vectors. Under a mild regularity assumption, we find that the candidate surface is indeed an event horizon and the disformed Kerr metric is therefore a black hole quite distinct from the Kerr solution.

A note on distinct distances

We show that, for a constant-degree algebraic curve γ in ℝD, every set of n points on γ spans at least Ω(n4/3) distinct distances, unless γ is an algebraic helix, in the sense of Charalambides [2]. This improves the earlier bound Ω(n5/4) of Charalambides [2].We also show that, for every set P of n points that lie on a d-dimensional constant-degree algebraic variety V in ℝD, there exists a subset S ⊂ P of size at least Ω(n4/(9+12(d−1))), such that S spans $\left({\begin{array}{*{20}{c}} {|S|} \\ 2 \\\end{array}} \right)$ distinct distances. This improves the earlier bound of Ω(n1/(3d)) of Conlon, Fox, Gasarch, Harris, Ulrich and Zbarsky [4].Both results are consequences of a common technical tool.

Thermodynamic Performance Analysis of Hydrofluoroolefins (HFO) Refrigerants in Commercial Air-Conditioning Systems for Sustainable Environment

Global warming is one of most severe environmental concerns that our planet is facing today. One of its causes is the previous generation of refrigerants that, upon release, remain in the atmosphere for longer periods and contribute towards global warming. This issue could potentially be solved by replacing the previous generation’s high global warming potential (GWP) refrigerants with environmentally friendly refrigerants. This scenario requires an analysis of new refrigerants for a comparison of the thermodynamic properties of the previously used refrigerants. In the present research, a numerical study was conducted to analyze the thermodynamic performance of specifically low GWP hydrofluoroolefens (HFO) refrigerants for an actual vapor compression refrigeration cycle (VCRC) with a constant degree of 3 K superheat. The output parameters included the refrigeration effect, compressor work input, the coefficient of performance (COP), and the volumetric refrigeration capacity (VRC), all of which were calculated by varying the condenser pressure from 6 to 12 bars and vapor pressure from 0.7 to 1.9 bars. Results showed that R1234ze(Z) clearly possessed the desired thermodynamic performance. The drop in refrigeration effect for R1234ze(Z) was merely 14.6% less than that of R134a at a 12 bar condenser pressure; this was minimum drop among candidate refrigerants. The drop in the COP was the minimum for R1234ze(Z)—5.1% less than that of R134a at a 9 bar condenser pressure and 4.7% less than that of R134a at a 1.9 bar evaporator pressure, whereas the COP values of the other refrigerants dropped more drastically at higher condenser pressures. R1234ze(Z) possessed favorable thermodynamic characteristics, with a GWP of 7, and it can serve as an alternative refrigerant for refrigeration systems for a sustainable environment.