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Indonesia's palm oil plantation is dominated by three actors. Among three actors, the productivity of smallholder farmers has the lowest productivity. This study aims to analyze the value of technical efficiency and factors affecting the technical inefficiency of palm oil plantations in Indonesia by using the stochastic frontier analysis based on the translog production function. The data used in this study are taken from the Central Statistics Agency (Agricultural Business Household Income Survey) in 2013. The number of samples used was 14,367 farmers. The results revealed that the average value of technical efficiency (58.32%) is still far to reach its optimal, showing that there is still to increase in the efficiency of palm oil plantations in Indonesia. The production function suggests that increasing the number of trees can help to increase the number of outputs. To enhance the technical efficiency, education, age, planting system, seed quality, extension service, and plasma farmer are the significant factors. [ABSTRACT FROM AUTHOR]

In this paper, we establish a deformation theory for Dolbeault cohomology classes valued in holomorphic tensor bundles. We prove the extension equation which will play the role of Maurer–Cartan equation. Following the classical theory of Kodaira–Spencer–Kuranishi, we construct a canonical complete family of deformations by using the power series method. We also prove a simple relation between the existence of deformations and the varying of the dimensions of Dolbeault cohomology. The deformations of (p, q)-forms is shown to be unobstructed under some mild conditions. By analyzing Nakamura's example of complex parallelizable manifolds, we will see that the deformation theory developed in this work provides precise explanations to the jumping phenomenon of Dolbeault cohomology. [ABSTRACT FROM AUTHOR]

A Kummer-faithful field k is a perfect field such that the Kummer map associated to G is injective for every finite extension K of k and every semi-abelian variety G over K. A typical example of a Kummer-faithful field of characteristic zero is a sub-p-adic field for some prime number p. In particular, every number field is Kummer-faithful. In this paper, we give a construction of a Kummer-faithful field which is an infinite algebraic extension of the field of rational numbers. Moreover, we give some examples of Kummer-faithful fields which are not sub-p-adic by using the constructions. [ABSTRACT FROM AUTHOR]

Axions, periodic scalar fields coupled to gauge fields through the instanton density, have a rich variety of higher-form global symmetries. These include a two-form global symmetry, which measures the charge of axion strings. As we review, these symmetries typically combine into a higher-group, a kind of non-abelian structure where symmetries that act on operators of different dimensions, such as points, lines, and strings, are mixed. We use this structure to derive model independent constraints on renormalization group flows that realize theories of axions at long distances. These give universal inequalities on the energy scales where various infrared symmetries emerge. For example, we show that in any UV completion of axion-Yang-Mills, the energy scale at which axion strings can decay is always larger than the mass scale of charged particles. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new set of modular-invariant phase factors for orbifolds with trivially-acting subgroups, analogous to discrete torsion and generalizing quantum symmetries. After describing their basic properties, we generalize decomposition to include orbifolds with these new phase factors, making a precise proposal for how such orbifolds are equivalent to disjoint unions of other orbifolds without trivially-acting subgroups or one-form symmetries, which we check in numerous examples. [ABSTRACT FROM AUTHOR]

Cochains in commutative semigroup cohomology satisfy symmetry conditions that have only been ascertained in dimensions n ≤ 4 . This article studies how symmetry conditions are passed from one dimension to the next, and proposes two conjectures about the appropriate conditions for dimensions 5 and 6. [ABSTRACT FROM AUTHOR]

Such situations lead naturally to the operators HT ht and HT ht on HT ht . In [[44]], Mario introduces a generalization of the systems of the words HT ht , HT ht HT ht (see (1)) in the signature of completely regular semigroups, and calls the varieties of left and right normal orthogroups together with the varieties defined by any one of the generalized versions of the identities in (1) I canonical varieties i . [Extracted from the article]

We prove a version of Furstenberg’s ergodic theorem with restrictions on return times. More specifically, for a measure preserving system ( X, B, μ,T), integers 0 ≤ j < k, and E ⊂ X with μ(E) > 0, we show that there exists n ≡ j (mod k) with ώ( E ∩ T -nE ∩ T -2nE ∩ T -3nE) > 0, so long as T k is ergodic. This result requires a deeper understanding of the limit of some nonconventional ergodic averages and the introduction of a new class of systems, the ‘Quasi-Affine Systems’. [ABSTRACT FROM AUTHOR]

It is proved that the universally solvable embedding problem with cyclic kernel of odd order is semidirect. Bibliography: 4 titles. [ABSTRACT FROM AUTHOR]

We review several known categorification procedures, and introduce a functorial categorification of group extensions (Section 4.1) with applications to non-Abelian group cohomology (Section 4.2). The obstruction to the existence of group extensions (Section 4.2.4, Equation (9)) is interpreted as a “coboundary” condition (Proposition 4.5). [ABSTRACT FROM AUTHOR]

We show that a p-analogue to the elementary type conjecture is not true. In fact, p-quaternionic pairings of non-elementary type are constructed for every prime p≥ 3. [ABSTRACT FROM AUTHOR]

This paper presents a special (six-dimensional) representation of Lie algebra of the nonrelativistic analog of the conformal group, 15-parameter extended Galilean–Newtonian group. In contrast to the conventional (four-dimensional) representation, the found set of infinitesimal operators can be obviously extended to the representation of the Lie algebra of the nonrelativistic analogue of the 16-parameters extended conformal group. In conclusion, the principal point of Klein's Erlangen concept ("Given a manifold and a transformation group acting on it") and the author's thesis "space-time is a metaphysical ghost that should be excluded from the scientific description of nature" are compared. [ABSTRACT FROM AUTHOR]

We study Galois actions on 2+1D topological quantum field theories (TQFTs), characterizing their interplay with theory factorization, gauging, the structure of gapped boundaries and dualities, 0-form symmetries, 1-form symmetries, and 2-groups. In order to gain a better physical understanding of Galois actions, we prove sufficient conditions for the preservation of unitarity. We then map out the Galois orbits of various classes of unitary TQFTs. The simplest such orbits are trivial (e.g., as in various theories of physical interest like the Toric Code, Double Semion, and 3-Fermion Model), and we refer to such theories as unitary "Galois fixed point TQFTs". Starting from these fixed point theories, we study conditions for preservation of Galois invariance under gauging 0-form and 1-form symmetries (as well as under more general anyon condensation). Assuming a conjecture in the literature, we prove that all unitary Galois fixed point TQFTs can be engineered by gauging 0-form symmetries of theories built from Deligne products of certain abelian TQFTs. [ABSTRACT FROM AUTHOR]

The feasibility of establishing a proper notion of a distinguishable object in the context of the de Broglie–Bohm approach to quantum mechanics seems, at first sight, uncontroversial by virtue of the fact that this theory can supposedly be interpreted in terms of a system of objective particles distinguished by individuating properties. However, after conducting a critical revision and evaluation of this trivial interpretation, and having assessed different alternatives that have been proposed in recent literature, I argue that within this theory an appropriate notion of a distinguishable object can only be articulated by means of the following theoretical and metaphysical strategies: firstly, by appealing to a pre-existing, symmetrized Bohmian framework that is empirically indistinguishable but physically distinguishable from the standard Bohmian formulation; and secondly, by suggesting a different interpretation of this symmetrized formulation based upon a relational notion of the distinguishable object that can only be appropriately conceived from a structuralist point of view. [ABSTRACT FROM AUTHOR]

Motivated by the recent experimental progress on the B-meson decay anomalies (in particular the angular observables in B → K ∗ μ μ ), we rely on a simplified-model approach to study the prospects of vector leptoquarks in what concerns numerous flavour observables, identifying several promising decay modes which would allow to (indirectly) probe such an extension. Our findings suggest that the confirmation of the B-meson decay anomalies, in parallel with positive signals (at Belle II or LHCb) for τ → ϕ μ , B (s) -meson decays to τ + τ - and τ + μ - ( τ + e - ) final states, as well as an observation of certain charged lepton flavour violation decays (at COMET or Mu2e), would contribute to strengthen the case for this scenario. We also illustrate how the evolution of the experimental determination of R D (∗) could be instrumental in falsifying an explanation of the anomalous B-meson decay data via a vector V 1 leptoquark. [ABSTRACT FROM AUTHOR]

Objective: Pediatric patients spend significant time on maintenance hemodialysis (HD) and traveling. They are often not capable of participating in sports activities. To assess the effects of exercise training during HD on dialysis efficacy in children and adolescents, we set up a multi-center randomized controlled trial (RCT). Methods: Patients on HD, age 6 to 18 years, were randomized either to 3× weekly bicycle ergometer training or to no training during HD for 12 weeks. Change in single-pool Kt/V (spKt/V) was the primary outcome parameter. Results: We randomized 54 patients of whom 45 qualified (23 in the intervention and 22 in the waiting control group, 14.5 ± 3.01 years, 32 male and 13 female) for the intention-to-treat (ITT) population. Only 26 patients finished study per-protocol (PP). Training was performed for an average of 11.96 weeks (0.14–13.14) at 2.08 ± 0.76 times per week and for a weekly mean of 55.52 ± 27.26 min. Single-pool Kt/V was similar in the intervention compared to the control group (1.70 [0.33] vs. 1.79 [0.55]) at V0 and (1.70 [0.36] vs. 1.71 [0.51]) at V1; secondary endpoints also showed no difference in both ITT and PP analysis. No significant adverse events were reported. No bleeding or needle dislocation occurred in 1670 training sessions. Conclusions: Intradialytic bicycle training is safe, but does not improve dialysis efficacy and physical fitness. However, the study can be considered underpowered, particularly because of high dropout rates. Future studies need better strategies to increase motivation and compliance and other more effective/intensive exercise measures should be evaluated. Trial registration: The trial was registered in ClinicalTrials.Gov (Clinicaltrials.gov identifier: NCT01561118) on March 22, 2012. [ABSTRACT FROM AUTHOR]

We calculate the spectrum of the diagram for each finite 3-transposition group. Such graphs with a given minimum eigenvalue have occurred in the context of compact Griess subalgebras of vertex operator algebras. [ABSTRACT FROM AUTHOR]

We describe the construction of CMC surfaces with symmetries in S 3 and ℝ 3 using a CMC quadrilateral in a fundamental tetrahedron of a tessellation of the space. The fundamental piece is constructed by the generalized Weierstrass representation using a geometric flow on the space of potentials. [ABSTRACT FROM AUTHOR]

Background: Total knee arthroplasty (TKA) is one of the most commonly used procedures in orthopedics. However, whether different would closure positions affect the clinical outcomes after TKA remains controversial. We conducted a meta-analysis of randomized controlled trials (RCT) to assess the effect of wound closure position on clinical TKA outcomes. Methods: Embase, PubMed, and the Cochrane Library databases were systematically searched. A systematic review and meta-analysis of all RCTs were performed to prove the role of different wound closure positions on TKA. Results: Five RCTs containing 389 patients were included. Surgical closure of 90° flexion in TKA was associated with higher post-operative range-of-motion (ROM) at post-operative 4 weeks, lower VAS post-operative pain scores 4 weeks and 3 months, better peak torque difference of flexor muscle strength at 60 and 180°/s angular velocities between the flexion and the extension groups, and better total work difference of flexor muscle strength at 180°/s angular velocity. The American Knee Society Score did not show any significant difference between two closure techniques. No complications were described in the literature review. Conclusions: Wound closure in 90° flexion during TKA may provide better postoperative ROM, higher pain relief, preferable muscle strength improvement in short-term follow-up, and no increase in the risks of wound complications. Level of evidence: Level II. [ABSTRACT FROM AUTHOR]

The simple symplectic group Sp(8, 2) has 11 conugacy classes of maximal subgroups. The fourth maximal subgroup of Sp(8, 2) is a group of the form 2 10 : A 8 : = G ¯. In this paper we study this group, where we determine its conjugacy classes and character table using the coset analysis technique together with Clifford–Fischer Theory. We determined the inertia factor groups of G ¯ and there are 7 such groups having the forms: H 1 = A 8 , H 2 = 2 3 : G L (3 , 2) , H 3 = 2 4 : (S 3 × S 3) , H 4 = 2 3 : S 4 , H 5 = S 5 , H 6 = (S 3 × S 3) : 2 and H 7 = 2 × S 4. The character table of G ¯ is a 81 × 81 complex valued matrix, while the Fischer matrices are all integer valued matrices with sizes ranging from 1 to 16. [ABSTRACT FROM AUTHOR]

This paper describes a generalization of decomposition in orbifolds. In general terms, decomposition states that two-dimensional orbifolds and gauge theories whose gauge groups have trivially-acting subgroups decompose into disjoint unions of theories. However, decomposition can be, at least naively, broken in orbifolds if the orbifold has discrete torsion in the trivially-acting subgroup. (Formally, this breaks finite global one-form symmetries.) Nevertheless, even in such cases, one still sees rudiments of decomposition. In this paper, we generalize decomposition in orbifolds to include such examples of discrete torsion, which we check in numerous examples. Our analysis includes as special cases (and in one sense generalizes) quantum symmetries of abelian orbifolds. [ABSTRACT FROM AUTHOR]

We study higher symmetries and anomalies of 4d so (2nc) gauge theory with 2nf flavors. We find that they depend on the parity of nc and nf, the global form of the gauge group, and the discrete theta angle. The contribution from the fermions plays a central role in our analysis. Furthermore, our conclusion applies to N = 1 supersymmetric cases as well, and we see that higher symmetries and anomalies match across the Intriligator-Seiberg duality between so (2nc) ↔ so (2nf − 2nc + 4). [ABSTRACT FROM AUTHOR]

We prove a structure theorem for the isometry group Iso (M , g) of a compact Lorentz manifold, under the assumption that a closed subgroup has exponential growth. We don't assume anything about the identity component of Iso (M , g) , so that our results apply for discrete isometry groups. We infer a full classification of lattices that can act isometrically on compact Lorentz manifolds. Moreover, without any growth hypothesis, we prove a Tits alternative for discrete subgroups of Iso (M , g) . [ABSTRACT FROM AUTHOR]

Motivated by the work in Li et al. (2019), this paper deals with the theory of the braids from chromatic configuration spaces. These kinds of braids possess the property that some strings of each braid may intersect together and can also be untangled, so they are quite different from the ordinary braids in the sense of Artin (1925). This enriches and extends the theory of ordinary braids. [ABSTRACT FROM AUTHOR]

The phase space of general relativity in a finite subregion is characterized by edge modes localized at the codimension-2 boundary, transforming under an infinite-dimensional group of symmetries. The quantization of this symmetry algebra is conjectured to be an important aspect of quantum gravity. As a step towards quantization, we derive a complete classification of the positive-area coadjoint orbits of this group for boundaries that are topologically a 2-sphere. This classification parallels Wigner's famous classification of representations of the Poincaré group since both groups have the structure of a semidirect product. We find that the total area is a Casimir of the algebra, analogous to mass in the Poincaré group. A further infinite family of Casimirs can be constructed from the curvature of the normal bundle of the boundary surface. These arise as invariants of the little group, which is the group of area-preserving diffeomorphisms, and are the analogues of spin. Additionally, we show that the symmetry group of hydrodynamics appears as a reduction of the corner symmetries of general relativity. Coadjoint orbits of both groups are classified by the same set of invariants, and, in the case of the hydrodynamical group, the invariants are interpreted as the generalized enstrophies of the fluid. [ABSTRACT FROM AUTHOR]

We classify various types of graded extensions of a finite braided tensor category B in terms of its 2-categorical Picard groups. In particular, we prove that braided extensions of B by a finite group A correspond to braided monoidal 2-functors from A to the braided 2-categorical Picard group of B (consisting of invertible central B -module categories). Such functors can be expressed in terms of the Eilnberg-Mac Lane cohomology. We describe in detail braided 2-categorical Picard groups of symmetric fusion categories and of pointed braided fusion categories. [ABSTRACT FROM AUTHOR]

Given a pair of an ergodic measured discrete equivalence relation R and a subrelation S ⊂ R of finite index, a classification of the inclusion up to orbit equivalence will be discussed. In case of amenable and type III0 relations, the orbit equivalence classes of inclusions will be completely classified in terms of a collection of a subgroup H and a normal subgroup G 0 of a finite group G and an ergodic group ( G/G 0) extension of a nonsingular flow. This is a generalization of Krieger’s theorem by which orbit equivalence classes of single relations were classified. Due to this result, essential type III inclusions will be made clear. [ABSTRACT FROM AUTHOR]

We derive a Chebotarev Theorem for finite homogeneous extensions of shifts of finite type. These extensions are of the form $$\tilde \sigma $$ : X×G/H→X×G/H where $$\tilde \sigma $$ ( x, gH)=(σ x, α( x) gH), for some finite group G and subgroup H. Given a σ-closed orbit τ, the periods of the $$\tilde \sigma $$ -closed orbits covering τ define a partition of the integer | G/H|. The theorem then gives us an asymptotic formula for the number of closed orbits with respect to the various partitions of the integer | G/H|. We apply our theorem to the case of a finite extension and of an automorphism extension of shifts of finite type. We also give a further application to 'automorphism extensions' of hyperbolic toral automorphisms. [ABSTRACT FROM AUTHOR]

The article discusses the development of outer finitary automorphism groups. It says that FAutG, a subgroup of G finitary automorphism, is an Abelian group extension and locally finite group extension. It mentions that FOutG, a periodic quotient FautG group, is implied as a locally infinite group. Moreover, conjugation of FC(G) the FC-center of G is also presented.

We present a modified age-structured SIR model based on known patterns of social contact and distancing measures within Washington, USA. We find that population age-distribution has a significant effect on disease spread and mortality rate, and contribute to the efficacy of age-specific contact and treatment measures. We consider the effect of relaxing restrictions across less vulnerable age-brackets, comparing results across selected groups of varying population parameters. Moreover, we analyze the mitigating effects of vaccinations and examine the effectiveness of age-targeted distributions. Lastly, we explore how our model can applied to other states to reflect social-distancing policy based on different parameters and metrics. [ABSTRACT FROM AUTHOR]

A mixed lattice group is a generalization of a lattice ordered group. The theory of mixed lattice semigroups dates back to the 1970s, but the corresponding theory for groups and vector spaces has been relatively unexplored. In this paper we investigate the basic structure of mixed lattice groups, and study how some of the fundamental concepts in Riesz spaces and lattice ordered groups, such as the absolute value and other related ideas, can be extended to mixed lattice groups and mixed lattice vector spaces. We also investigate ideals and study the properties of mixed lattice group homomorphisms and quotient groups. Most of the results in this paper have their analogues in the theory of Riesz spaces. [ABSTRACT FROM AUTHOR]

For symmorphic crystalline interacting gapped systems we derive a classification under adiabatic evolution. This classification is complete for non-degenerate ground states. For the degenerate case we discuss some invariants given by equivariant characteristic classes. We do not assume an emergent relativistic field theory nor that phases form a topological spectrum. We also do not restrict to systems with short-range entanglement, stability against stacking with trivial systems nor assume the existence of quasi-particles as is done in SPT and SET classifications respectively. Using a slightly generalized Bloch decomposition and Grassmanians made out of ground state spaces, we show that the P-equivariant cohomology of a d-dimensional torus gives rise to different interacting phases, where P denotes the point group of the crystalline structure. We compare our results to bosonic symmorphic crystallographic SPT phases and to non-interacting fermionic crystallographic phases in class A. Finally we discuss the relation of our assumptions to those made for crystallographic SPT and SET phases. [ABSTRACT FROM AUTHOR]

We examine various properties of double field theory and the doubled string sigma model in the context of geometric quantisation. In particular we look at T-duality as the symplectic transformation related to an alternative choice of polarisation in the construction of the quantum bundle for the string. Following this perspective we adopt a variety of techniques from geometric quantisation to study the doubled space. One application is the construction of the “double coherent state” that provides the shortest distance in any duality frame and a “stringy deformed” Fourier transform. [ABSTRACT FROM AUTHOR]

We wish to investigate continuous fields of the Cuntz algebras. The Cuntz algebras O n + 1 , n ≥ 1 play an important role in the theory of operator algebras, and they are characterized by their K-groups K 0 (O n + 1) = Z n , the cyclic groups of order n ≥ 1 . Since the mod n K-group for a compact Hausdorff space can be realized by the K-group of the trivial continuous field of O n + 1 over the space, one can regard O n + 1 as a noncommutative analogue of the Moore space of Z n , and classifying continuous fields of the Cuntz algebras is an interesting problem. M. Dadarlat classifies these fields which are constructed from the vector bundles of rank n + 1 , and he also showed that not every continuous field comes from the vector bundle. For a continuous field of O n + 1 over a finite CW complex, we introduce a topological invariant, which is an element in Dadarlat–Pennig's generalized cohomology group, and prove that the invariant is trivial if and only if the field comes from a vector bundle via Pimsner's construction. [ABSTRACT FROM AUTHOR]

It is well known that the set of isomorphism classes of extensions of groups with abelian kernel is characterized by the second cohomology group. In this paper we generalise this characterization of extensions to a natural class of extensions of monoids, the cosetal extensions. An extension is cosetal if for all g , g ′ ∈ G in which e (g) = e (g ′) , there exists a (not necessarily unique) n ∈ N such that g = k (n) g ′ . These extensions generalise the notion of special Schreier extensions, which are themselves examples of Schreier extensions. Just as in the group case where a semidirect product could be associated to each extension with abelian kernel, we show that to each cosetal extension (with abelian group kernel), we can uniquely associate a weakly Schreier split extension. The characterization of weakly Schreier split extensions is combined with a suitable notion of a factor set to provide a cohomology group granting a full characterization of cosetal extensions, as well as supplying a Baer sum. [ABSTRACT FROM AUTHOR]

Let G 2 be a group which acts trivially on an abelian group G 1 . According to the Schreier's Theorem, each 2-cocycle ε ∈ Z 2 (G 2 , G 1) determines a group G ε which is a central extension of G 1 by G 2 , and we will denote this group by G 1 × ε G 2 and call it the perturbed direct product of G 1 by G 2 under ε . The aim of this paper is to study properties of the perturbed direct products. For two distinct 2-cocycles ε 1 and ε 2 , we find necessary and sufficient conditions for G 1 × ε 1 G 2 to be isomorphic to G 1 × ε 2 G 2 . Furthermore, we obtain some results about decompositions for a given perturbed direct product G 1 × ε G 2 when G 1 or G 2 is a nontrivial direct product. [ABSTRACT FROM AUTHOR]

Fractional statistics is one of the most intriguing features of topological phases in 2D. In particular, the so-called non-Abelian statistics plays a crucial role towards realizing topological quantum computation. Recently, the study of topological phases has been extended to 3D and it has been proposed that loop-like extensive objects can also carry fractional statistics. In this work, we systematically study the so-called three-loop braiding statistics for 3D interacting fermion systems. Most surprisingly, we discover new types of non-Abelian three-loop braiding statistics that can only be realized in fermionic systems (or equivalently bosonic systems with emergent fermionic particles). On the other hand, due to the correspondence between gauge theories with fermionic particles and classifying fermionic symmetry-protected topological (FSPT) phases with unitary symmetries, our study also gives rise to an alternative way to classify FSPT phases. We further compare the classification results for FSPT phases with arbitrary Abelian unitary total symmetry Gf and find systematical agreement with previous studies. Non-Abelian statistics plays a crucial role towards realizing topological quantum computation. Here, the authors discover new types of non-Abelian three-loop braiding statistics that can only be realized in 3D interacting fermionic systems. [ABSTRACT FROM AUTHOR]

In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact (U(1)) component, a Lorentz (SL(2, ℂ)) component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman-Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold. [ABSTRACT FROM AUTHOR]

We give a complete (global) characterization of C -perverse sheaves on semi-abelian varieties in terms of their cohomology jump loci. Our results generalize Schnell’s work on perverse sheaves on complex abelian varieties, as well as Gabber–Loeser’s results on perverse sheaves on complex affine tori. We apply our results to the study of cohomology jump loci of smooth quasi-projective varieties, to the topology of the Albanese map, and in the context of homological duality properties of complex algebraic varieties. [ABSTRACT FROM AUTHOR]