``Impression Zombies'', a type of malicious account designed to artificially inflate engagement metrics, have recently emerged as a significant threat on X (formerly Twitter). These accounts disseminate a high volume of low-quality, irrelevant posts, which degrade the user experience. This study aims (1) to quantitatively characterize their behavioral patterns and (2) to develop a method for detecting such accounts. To address the first objective, we collected data from 9,909 accounts and compared the characteristics of Impression Zombies and general users within this dataset. We find that, Impression Zombies post more than three times the average total number of posts per day and tend to gather followers by using phrases such as ``follow back.'' Addressing the second objective, we constructed a classification model for Impression Zombies that leverages the contextual incoherence often observed between parent posts and the replies from Impression Zombies. Experimental results show that our model achieved approximately 92\% accuracy in detecting Impression Zombies. This study provides the first quantitative insights into Impression Zombies and offers a practical framework for detect
DNS integrations leverage the discovery, trust, and uniqueness of the global Domain Name System with a linkage to another naming ecosystem, so the DNS name can help identify resources such as a cryptocurrency wallet or software component. While DNS ownership is verified at linkage creation, many ecosystems do not track subsequent DNS changes. The result is zombie linkages, where the DNS ownership has expired or changed, but the mapping to the linked resource persists. We define a threat model for DNS integrations, identifying five classes of attacks that leverage or exploit zombie linkages. We measure zombie occurrence across three DNS integrations -- Web PKI; ENS, a blockchain naming system; and Maven Central, a Java software repository. We show that zombies exist in every ecosystem, but at very different fractions -- zombies make up roughly 3% of TLS certificates for new domains, 24% of ENS on-chain imports, and 15% of Maven Central namespaces. We evaluate how integration design choices affect outcomes, with validate-once integrations (ENS on-chain, Maven Central) accumulating long-lasting zombies, linkages with expiration (Web PKI) limiting damage, while integrations that valida
We study zombies and survivor, a variant of the game of cops and robber on graphs. In this variant, the single survivor plays the role of the robber and attempts to escape from the zombies that play the role of the cops. The zombies are restricted, on their turn, to always follow an edge of a shortest path towards the survivor. Let $z(G)$ be the smallest number of zombies required to catch the survivor on a graph $G$ with $n$ vertices. We show that there exist outerplanar graphs and visibility graphs of simple polygons such that $z(G) = Θ(n)$. We also show that there exist maximum-degree-$3$ outerplanar graphs such that $z(G) = Ω\left(n/\log(n)\right)$. Let $z_L(G)$ be the smallest number of lazy zombies (zombies that can stay still on their turn) required to catch the survivor on a graph $G$. We establish that lazy zombies are more powerful than normal zombies but less powerful than cops. We prove that $z_L(G) = 2$ for connected outerplanar graphs. We show that $z_L(G)\leq k$ for connected graphs with treedepth $k$. This result implies that $z_L(G)$ is at most $(k+1)\log n$ for connected graphs with treewidth $k$, $O(\sqrt{n})$ for connected planar graphs, $O(\sqrt{gn})$ for conne
We suggest that qualia have a causally efficacious role in quantum mechanics; an occurrence which explains how information about qualia can enter the physical environment. This is compatible with the unitary time-evolution of the quantum state if qualia are understood as effecting the beables of the de Broglie-Bohm interpretation or wavefunction collapse process rather than at the wavefunction level. We furthermore suggest that not all quantum states are consistent with qualia. If this is the case, the standard wavefunction collapse postulates of the Copenhagen interpretation will fail to select only those states which are consistent with qualia, and the Born-rule must be modified if wavefunction collapse is to generate the correct dynamical histories across time. This new model which includes qualia clearly demonstrates how non-linear and self-referential phenomena can occur, despite the linear, deterministic time-evolution of the wavefunction. We reject the notion that physical matter operates independently of qualia, and find that the main evidence for epiphenomenalism i.e. the causal closure of the underlying physical time-evolution, has failed to take into consideration fine-t
In pop culture, there are many strategies to curtail zombie apocalypses. However, it remains unclear what routes we should take to eliminate zombies effectively and affordably. So, we created a mathematical model to examine interventions that armed adults with steelhead axes or provided enough ammunition and a 9mm handgun to kill zombies in either a "single-tap" or "double-tap". We investigate each case over two years under slow, moderate speed, and fast zombies scenarios. We quantify health burden by zombies averted, disability-adjusted life-years averted, and determine cost-effectiveness using the incremental cost-effectiveness ratio. Our predictions show the single=tap intervention is the best for stopping the zombie apocalypse, as it would avert hundreds of millions of zombies and deaths while also being the most cost-effective intervention. Altogether, this suggests conserving ammunition and supplying ranged weapons would be an effective use of limited resources in the event of a zombie uprising.
In Zombies and Survivors, a set of zombies attempts to eat a lone survivor loose on a given graph. The zombies randomly choose their initial location, and during the course of the game, move directly toward the survivor. At each round, they move to the neighbouring vertex that minimizes the distance to the survivor; if there is more than one such vertex, then they choose one uniformly at random. The survivor attempts to escape from the zombies by moving to a neighbouring vertex or staying on his current vertex. The zombies win if eventually one of them eats the survivor by landing on their vertex; otherwise, the survivor wins. The zombie number of a graph is the minimum number of zombies needed to play such that the probability that they win is at least 1/2. This variant of the game was recently investigated for several graph families, such as cycles, hypercubes, incidence graphs of projective planes, and grids $P_n \square P_n$. However, unfortunately, still very little is known for toroidal grids $C_n \square C_n$: the zombie number of $C_n \square C_n$ is at least $\sqrt n/(ω\log n)$, where $ω= ω(n)$ is any function going to infinity as $n \to \infty$, and no upper bound is know
We consider a new probabilistic graph searching game played on graphs, inspired by the familiar game of Cops and Robbers. In Zombies and Survivors, a set of zombies attempts to eat a lone survivor loose on a given graph. The zombies randomly choose their initial location, and during the course of the game, move directly toward the survivor. At each round, they move to the neighbouring vertex that minimizes the distance to the survivor; if there is more than one such vertex, then they choose one uniformly at random. The survivor attempts to escape from the zombies by moving to a neighbouring vertex or staying on his current vertex. The zombies win if eventually one of them eats the survivor by landing on their vertex; otherwise, the survivor wins. The zombie number of a graph is the minimum number of zombies needed to play such that the probability that they win is strictly greater than 1/2. We present asymptotic results for the zombie numbers of several graph families, such as cycles, hypercubes, incidence graphs of projective planes, and Cartesian and toroidal grids.
Recent advances in LLMs have sparked a debate on whether they understand text. In this position paper, we argue that opponents in this debate hold different definitions for understanding, and particularly differ in their view on the role of consciousness. To substantiate this claim, we propose a thought experiment involving an open-source chatbot $Z$ which excels on every possible benchmark, seemingly without subjective experience. We ask whether $Z$ is capable of understanding, and show that different schools of thought within seminal AI research seem to answer this question differently, uncovering their terminological disagreement. Moving forward, we propose two distinct working definitions for understanding which explicitly acknowledge the question of consciousness, and draw connections with a rich literature in philosophy, psychology and neuroscience.
This study introduces a unique active matter system as an application of the pedestrian collision avoidance paradigm, that proposes dynamically adjusting the desired velocity. We present a fictitious human-zombie scenario set within a closed geometry, combining prey-predator behavior with a one-way contagion process that can transform prey into predators. The system demonstrates varied responses, in cases where agents have the same maximum speeds, a single zombie always catches a human, whereas two zombies never catch a single human. As the number of human agents increases, observables, such as the final fraction of zombie agents and total conversion times, exhibit a significant change in the system's behavior at intermediate density values. Most notably, there is evidence of a first-order phase transition when the mean population speed is analyzed as an order parameter.
We consider the game of Zombies and Survivors as introduced by Fitzpatrick, Howell, Messinger and Pike (2016) This is a variation of the game Cops and Robber where the zombies (in the cops' role) are of limited intelligence and will always choose to move closer to a survivor (who takes on the robber's role). The zombie number of a graph is defined to be the minimum number of zombies required to guarantee the capture of a survivor on the graph. In this paper, we show that the zombie number of the Cartesian product of $n$ non-trivial trees is exactly $\lceil 2n/3 \rceil$. This settles a conjecture by Fitzpatrick et. al. (2016) that this is the zombie number for the $n$-dimensional hypercube. In proving this result, we also discuss other variations of Cops and Robber involving active and flexible players.
"Zombies and Survivor" is a variant of the well-studied game of "Cops and Robber" where the zombies (cops) can only move closer to the survivor (robber). We consider the deterministic version of the game where a zombie can choose their path if multiple options are available. The zombie number, like the cop number, of a graph is the minimum number of zombies, or cops, required to capture the survivor. In this short note, we solve a question by Fitzpatrick et al., proving that the zombie number of the Cartesian product of two graphs is at most the sum of their zombie numbers. We also give a simple graph family with cop number $2$ and an arbitrarily large zombie number.
We compare two kinds of pursuit-evasion games played on graphs. In Cops and Robbers, the cops can move strategically to adjacent vertices as they please, while in a new variant, called deterministic Zombies and Survivors, the zombies (the counterpart of the cops) are required to always move towards the survivor (the counterpart of the robber). The cop number of a graph is the minimum number of cops required to catch the robber on that graph; the zombie number of a graph is the minimum number of zombies required to catch the survivor on that graph. We answer two questions from the 2016 paper of Fitzpatrick, Howell, Messinger, and Pike. We show that for any $m \ge k \ge 1$, there is a graph with zombie number $m$ and cop number $k$. We also show that the zombie number of the $n$-dimensional hypercube is $\lceil 2n/3\rceil$.
Defending against botnets has always been a cat and mouse game. Cyber-security researchers and government agencies attempt to detect and take down botnets by playing the role of the cat. In this context, a lot of work has been done towards reverse engineering certain variants of malware families as well as understanding the network protocols of botnets to identify their weaknesses (if any) and exploit them. While this is necessary, such an approach offers the botmasters the ability to quickly counteract the defenders by simply performing small changes in their arsenals. We attempt a different approach by actually taking the role of the Botmaster, to eventually anticipate his behavior. That said, in this paper, we present a novel computational trust mechanism for fully distributed botnets that allows for a resilient and stealthy management of the infected machines (zombies). We exploit the highly researched area of computational trust to create an autonomous mechanism that ensures the avoidance of common botnet tracking mechanisms such as sensors and crawlers. In our futuristic botnet, zombies are both smart and cautious. They are cautious in the sense that they are careful with who
We use a popular fictional disease, zombies, in order to introduce techniques used in modern epidemiology modelling, and ideas and techniques used in the numerical study of critical phenomena. We consider variants of zombie models, from fully connected continuous time dynamics to a full scale exact stochastic dynamic simulation of a zombie outbreak on the continental United States. Along the way, we offer a closed form analytical expression for the fully connected differential equation, and demonstrate that the single person per site two dimensional square lattice version of zombies lies in the percolation universality class. We end with a quantitative study of the full scale US outbreak, including the average susceptibility of different geographical regions.
In this paper we present construction systems -- tuples $(X, BB, \oplus, ν)$ comprising objects, building blocks, an assembly operation, and a joining multiplicity -- as a general algebraic framework for studying how complex objects are built from simpler parts. To each construction system we associate a toric ideal, a toric variety, and a matroid, obtaining analytical bounds on the growth function $N(a)$ (the number of objects of construction complexity $\leq a$) purely from the design signature $(m, ν, n_0)$. For systems equipped with a type system and valence bounds, we define the composition polytope $P_{\mathrm{val}} \subset \mathbb{R}^m$, whose integer points count the feasible compositions. Compositions outside $P_{\mathrm{val}}$ -- termed zombies -- are combinatorially valid but physically unrealisable. We prove that the zombie classification is sound (zero false positives) and conservative: the true infeasibility rate is at least as high as the polytope predicts. Specialising to the molecular graph assembly system of Morales Parra et al. ($m = 19$ bond types, $5$ atom types with valences $1$--$4$), we identify a composition polytope whose lattice points capture the physica
We study a variant of the stochastic SIR model on graphs that has previously been introduced in the physics literature for modelling zombie outbreaks and here referred to as the Zombie Infection Model (ZIM). In this model, initially each node of a graph is either susceptible, infected or removed. As in the SIR model, a susceptible node becomes infected at rate $λ$ times the number of its infected neighbours. Moreover, in the ZIM, an infected node is removed at rate $1$ times the number of its susceptible neighbours. This process exhibits rich and sometimes counterintuitive behaviour. By combining various coupling techniques, we provide a rigorous mathematical analysis of the model, focusing on monotonicity properties and the probability of the infection spreading indefinitely. One of our main results is that this probability is monotone with respect to an increase of $λ$ for the process on trees, but that there are graphs of bounded degree for which it is continuous and yet not monotone. We also establish bounds on this probability for the process on general graphs, and derive more precise results for complete graphs, regular trees, and the $d$-dimensional integer lattice.
Self-evolving LLM agents update their internal state across sessions, often by writing and reusing long-term memory. This design improves performance on long-horizon tasks but creates a security risk: untrusted external content observed during a benign session can be stored as memory and later treated as instruction. We study this risk and formalize a persistent attack we call a Zombie Agent, where an attacker covertly implants a payload that survives across sessions, effectively turning the agent into a puppet of the attacker. We present a black-box attack framework that uses only indirect exposure through attacker-controlled web content. The attack has two phases. During infection, the agent reads a poisoned source while completing a benign task and writes the payload into long-term memory through its normal update process. During trigger, the payload is retrieved or carried forward and causes unauthorized tool behavior. We design mechanism-specific persistence strategies for common memory implementations, including sliding-window and retrieval-augmented memory, to resist truncation and relevance filtering. We evaluate the attack on representative agent setups and tasks, measurin
Recent advancements in LLM-based multi-agent systems have demonstrated remarkable collaborative capabilities across complex tasks. To improve overall efficiency, existing methods often rely on aggressive graph evolution among agents (e.g., node or edge pruning), which risks prematurely discarding valuable agents due to transient issues such as hallucinations or temporary knowledge gaps. However, such hard pruning overlooks the potential for ``zombie'' agents to recover and contribute in subsequent discussion rounds. In this paper, we propose AgentRevive, a Markov state-aware framework for resilient multi-agent evolution. Our approach dynamically manages agent collaboration through soft state transitions, implemented via two key components: (1) State-Aware Policy Learning: Agent states are divided into ``Active'', ``Standby'', and ``Terminated'' states, selectively propagating messages based on agent memory. The policy employs a risk estimator to optimize agent state transitions by assessing hallucination risk, minimizing the influence of unreliable nodes while safeguarding valuable ones. (2) State-Aware Edge Optimization: Subgraph edges are pruned according to states learned from t
In the damage variant of Cops and Robber, the \emph{damage number} \(\dmg(G)\) is the number of distinct vertices damaged by the robber under optimal play, with one cop minimizing and the robber maximizing this number. We introduce the \emph{zombie damage number} \(\zdmg(G)\), obtained by requiring the pursuer to move at every turn along a shortest path toward the survivor. The parameter therefore measures the cost of geodesic pursuit when the objective is containment rather than capture alone. We prove that \(\dmg(G)\leq\zdmg(G)\) and characterize the graphs with \(\zdmg(G)=0\). Geodesic pursuit incurs no additional damage on trees, and we determine the parameter exactly for paths, cycles, split graphs, and complete multipartite graphs. In particular, \(\zdmg(C_n)=n\) for \(n\geq5\), while \(\zdmg(K_{n_1,\ldots,n_k})=n_1+n_2-2\) when \(n_i\geq2\) for every \(i\). We also develop a nonbacktracking trace argument for sparse graphs. If \(G\) is connected, \(δ(G)\geq2\), and \(g(G)\geq5\), then every vertex is damaged, and hence \(\zdmg(G)=n(G)\). The same argument gives the sharp bound \(\zdmg(G)\geq g(G)\) for every connected graph of finite girth at least five. It follows that full
We adapt the social force model of crowd dynamics to capture the evacuation during a zombie outbreak from an academic building. Individuals navigate the building, opening doors, and evacuate to the nearest exit. Zombies chase the uninfected individuals, and once caught there is a probability of a susceptible individual being infected or killed, or for the zombie to be killed by the person being attacked. We find that the speed of the zombies plays a crucial role in the dynamics of the evacuation, the rate of infection, and the number of casualties during the outbreak. The model leads to insights that may be relevant to other, less fictitious, emergency situations.