We give a description of the boundary of a complex of free factors that is analogous to E. Klarreich's description of the boundary of a curve complex. The argument uses the geometry of folding paths developed by Bestvina and Feighn as well as structu...
A city is not a tree but a semi-lattice. To use a perhaps more familiar term, a city is a complex network. The complex network constitutes a unique topological perspective on cities and enables us to better understand the kind of problem a city is. T...
We study the query complexity analogue of the class TFNP of total search problems. We give a way to convert partial functions to total search problems under certain settings; we also give a way to convert search problems back into partial functions....
The Williamsburg Indoor Sports Complex makes it easy for families to stay active, healthy, and connected. Enjoy fitness, sports, and childcare—all in one convenient location.
Reservoir computing with optical devices offers an energy-efficient approach for time-series forecasting. Quantum dot lasers with feedback are modelled in this paper to explore the extent to which increased complexity in the charge carrier dynamics w...
An overarching challenge in rheology is to develop constitutive models for complex fluids for which we lack accurate first principles theory. A further challenge is that most experiments probing dynamical structure and rheology do so only in very sim...
We often add arithmetic to extend the expressiveness of query languages and study the complexity of problems such as testing query containment and finding certain answers in the framework of answering queries using views. When adding arithmetic compa...
complex tic, is a language disorder characterized by the involuntary repetition of syllables, words, or phrases. It has features resembling other complex
Eluder dimension and information gain are two widely used methods of complexity measures in bandit and reinforcement learning. Eluder dimension was originally proposed as a general complexity measure of function classes, but the common examples of wh...
Jan 2, 2026 · Staking being complex is also something I think should not be holding back a protocol like Reserve. If the gov/admin-key maintainers of this index think staking is complex, that would be bearish.
Globalised-civilisation interaction intensity grows exponentially, involving all dimensions and regions of planetary environment. The resulting dynamics of critically high, exploding complexity urgently needs consistent understanding and efficient...
A-posteriori probability (APP) receivers operating over multiple-input, multiple-output channels provide enhanced bit error rate (BER) performance at the cost of increased complexity. However, employing full APP processing over favorable transmission...
Consider a singular holomorphic map-germ $f: (X,\underline{0}) \to (\mathbb C,0)$ where $X$ is a singular complex analytic variety in $\mathbb C^N$, and another holomorphic map-germ $g: (X,\underline{0}) \to (\mathbb C,0)$ which is "sufficiently good...
Consider 2n points on the unit circle and a reference dissection D of the convex hull of the odd points. The accordion complex of D is the simplicial complex of subsets of pairwise noncrossing diagonals with even endpoints that cross a connected set...
We prove some new continuity results for the Julia sets $J$ and $J^{+}$ of the complex Hénon map $H_{c,a}(x,y)=(x^{2}+c+ay, ax)$, where $a$ and $c$ are complex parameters. We look at the parameter space of dissipative Hénon maps which have a fixed...
(Doesn't work anymore) (⭐ 180)
Given a locally finite cover of a simplicial complex by subcomplexes, Björner's version of the Nerve Theorem provides conditions under which the homotopy groups of the nerve agree with those of the original complex through a range of dimensions. We...
A matrix $T \in \M_n(\C)$ is \emph{UECSM} if it is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. We develop several techniques for studying this property in dimensions three and four. Among other things, we completely cha...
Classically, the time complexity of a first-order method is estimated by its number of gradient computations. In this paper, we study a more refined complexity by taking into account the `lingering' of gradients: once a gradient is computed at $x_k$,...
Considering electronic implications in the Information Society (IS) as a complex system, complexity science tools are used to describe the processes that are seen to be taking place. The sometimes troublesome relationship between the information and...
Complex structure formation and fast focusing of light inside or through turbid media is a challenging task due to refractive index heterogeneity, random light scattering and speckle noise formation. Here, we have proposed a weighted-mutation assiste...
We present the Benchmark of Information Retrieval (IR) tasks with Complex Objectives (BIRCO). BIRCO evaluates the ability of IR systems to retrieve documents given multi-faceted user objectives. The benchmark's complexity and compact size make it sui...
Mathematical ideas and approaches common in complexity-related fields have been fruitfully applied in experimental high energy physics also. We briefly review some of the cross-pollination that is occurring....
In this paper, we address a bicriteria network design problem that arises from practical applications in urban and rural public transportation planning. We establish the problem's complexity and demonstrate inapproximability results, highlighting the...
The linear FEAST algorithm is a method for solving linear eigenvalue problems. It uses complex contour integration to calculate the eigenvectors whose eigenvalues that are located inside some user-defined region in the complex plane. This makes it po...
We define the surface complex for $3$-manifolds and embark on a case study in the arena of Seifert fibered spaces. The base orbifold of a Seifert fibered space captures some of the topology of the Seifert fibered space, so, not surprisingly, the surf...
The Raven Rock Mountain Complex (RRMC), also known as Site R and simply The Rock, is a U.S. military installation with an underground nuclear bunker near
hello. I came to the realisation today that I have a saviour complex. I think I am morally superior than others. I was bullied, left out and treated like shit when I was a teen. As a young adult who...
Financial markets are well known examples of multi-fractal complex systems that have garnered much interest in their characterization through complex network theory. The recent studies have used correlation based distance metrics for defining and ana...
Networks are essential for analyzing complex systems. However, their growing size necessitates backbone extraction techniques aimed at reducing their size while retaining critical features. In practice, selecting, implementing, and evaluating the mos...
In one complex variable it is well known that if we consider the family of all holomorphic functions on the unit disc that fix the origin and with first derivative equal to 1 at the origin, then there exists a constant $ρ$, independent of the functi...
For more than two decades the Tevatron proton-antiproton collider was the centerpiece of the world's high energy physics program. The collider was arguably one of the most complex research instruments ever to reach the operation stage and is widely r...
Today's programmers can choose from an exceptional range of programming languages, each with its own traits, purpose, and complexity. A key aspect of a language's complexity is how hard it is to compile programs in the language. While most programmer...
We prove that the restricted normal holonomy group of a Kähler submanifold of the complex hyperbolic space $\mathbb{C}H^{n}$ is always transitive, provided the index of relative nullity is zero. This contrasts with the case of $\mathbb{C}P^{n}$, whe...
We investigate Cousin (bi-)complexes in the setting of motives. Over essentially smooth local schemes, the columns of the Cousin bicomplex with coefficients in any stable motivic homotopy type are shown to be acyclic. On the other hand, we also const...
In this thesis, the class of modules whose Cousin complexes have finitely generated cohomologies are studied as a subclass of modules which have uniform local cohomological annihilators and it is shown that these two classes coincide over local rings...
I got a notice via email a while back that the Apartment complex where I live in Denver was going to be installing "SmartHome" devices in my apartment. I didn't respond because I assumed I would have ...
A simplicial complex is d-collapsible if it can be reduced to an empty complex by repeatedly removing (collapsing) a face of dimension at most d-1 that is contained in a unique maximal face. We prove that the algorithmic question whether a given simp...
These are notes from a basic course in Several Complex Variables...
Sofic shifts are symbolic dynamical systems defined by the set of bi-infinite sequences on an edge-labeled directed graph, called a presentation. We study the computational complexity of an array of natural decision problems about presentations of so...